President Biden kicks off his final week in office on Monday with a robust defense of his foreign policy, arguing in a speech to be delivered in the afternoon that America has become stronger on his watch.

With just seven days left until he hands over the White House to President-elect Donald J. Trump, Mr. Biden hopes to use his remaining time to frame his historical legacy as a transformational leader who bolstered the United States at home and abroad even in just one term.

The effort gets underway at 2 p.m. on Monday with a speech at the State Department focused on what he sees as his successes in the international arena. He plans to say that he strengthened U.S. alliances both in Europe in the face of Russian aggression as well as in the Asian-Pacific amid the rise of China. At the same time, he plans to argue that America’s adversaries — particularly Russia, China and Iran — are all weaker than when he came to office.

“He’s going to ask the question: is America stronger than we were four years ago? And he’s going to answer the question with a definitive yes,” Jake Sullivan, his national security adviser, said in a preview on “State of the Union” on CNN on Sunday. “Our alliances are stronger, as I said before. Our enemies and competitors are weaker. We kept the nation out of war. Every element of American power is stronger today.”

The speech will be the first this week aimed at presenting the best case for Mr. Biden’s presidency as it comes to an end. He will deliver a broader televised farewell address to the nation in prime time on Wednesday evening, much as many presidents have done. He will also deliver speeches this week on his conservation record and at a farewell ceremony for the commander in chief at Joint Base Myers-Henderson Hall.

On foreign policy, Mr. Biden has presided over a tumultuous time and Mr. Trump blamed him for the wars in Ukraine and Gaza, although no U.S. troops are directly involved on the ground in either place. Some critics said the perception of a world aflame and spinning out of Mr. Biden’s control contributed to the erosion of his political popularity at home and ultimately his withdrawal from the election under pressure.

“The fact that Biden is handing the presidency back to his predecessor is in part a reflection of his foreign policy shortcomings,” said Peter Rough, director of the Center on Europe and Eurasia at the Hudson Institute and a former aide to President George W. Bush.

“For most of his time in office, Biden has been on the defensive, first in Ukraine and then in Gaza,” Mr. Rough continued. “The president’s 1990s-era liberal internationalism may have been well intentioned, but it always felt out of step to me with the power politics of the 2020s.”

Still, a new Gallup poll released on Monday showed that America’s standing in Europe has improved strikingly under Mr. Biden. Of 30 NATO allies surveyed, approval of U.S. leadership rose in all but four since 2020, Mr. Trump’s last year in office. Approval ratings rose by double digits in 20 of the 30 countries. In Germany, for instance, approval of U.S. leadership rose from just 6 percent under Mr. Trump to 52 percent under Mr. Biden.

In pulling U.S. troops out of Afghanistan and extricating America from a the longest war in its history, Mr. Biden finally accomplished what his two predecessors wanted to but did not. But the chaotic nature of the withdrawal did considerable damage to both his and the country’s standing in the world.

Mr. Biden rallied much of the world to stand up to Russia’s unprovoked full-scale invasion of Ukraine and reinvigorated NATO after ties frayed under Mr. Trump, even admitting two new members, Sweden and Finland. He steered tens of billions of dollars worth of American arms to Ukraine that helped thwart Moscow’s attempt to take over the country.

But Mr. Biden was criticized from two different directions; some complained he was too reticent to deliver more powerful weapons for fear of escalating with a nuclear superpower, while others complained that he was investing too much American treasure in someone else’s war. And after its initial stunning success, Ukraine’s defense has stalled and Mr. Trump is now promising to end the war with what are expected to be concessions to President Vladimir V. Putin of Russia.

The war in Gaza that followed the Hamas terrorist attack on Israel on Oct. 7, 2023, was the other dominating crisis of Mr. Biden’s tenure. He stood staunchly by Israel and provided weapons for its all-out assault on Hamas, but eventually grew frustrated with Prime Minister Benjamin Netanyahu of Israel who rebuffed American pressure to do more to curb civilian casualties and relieve humanitarian suffering.

Even now, in his final days, Mr. Biden is straining to seal an elusive cease-fire agreement that would end the fighting and result in the release of Israeli hostages held in Gaza, including a few with American citizenship. Mr. Sullivan said Sunday that U.S. negotiators were “very, very close” to a deal, but it was not clear it could be finalized by next Monday when Mr. Trump takes over.

As with Ukraine, Mr. Biden faced criticism from both directions. From one side, he was accused of not doing more to stop the killing of civilians and called “Genocide Joe” at protests. From the other side, he was faulted for putting pressure on Israel to restrain itself in the face of an existential terrorist threat.

High-level cease-fire talks appeared to be gaining momentum on Monday as Arab and American mediators pressed for an agreement to halt the fighting in Gaza and release hostages held by Hamas before President-elect Donald J. Trump assumes office on Jan. 20.

It was still unclear whether the parties had reached resolution on central disputes that have proved insurmountable in previous rounds of negotiations, but officials briefed on the talks have expressed cautious optimism in recent days about the possibility of concluding a deal.

For months, repeated rounds of talks have seen hopes rise only to be dashed days later, with both Israel and Hamas blaming the other for the impasse.

If a deal is achieved, it would bring some respite to Palestinians in Gaza, who have endured miserable conditions in displacement camps and relentless bombardments by Israel, and the families of hostages taken from Israel, who have suffered for months wondering about the fate of their loved ones.

Who are the players?

• The lead mediators in the talks are Qatar and Egypt, shuttling messages between Israel and Hamas. The Qatari prime minister, Sheikh Mohammed bin Abdulrahman bin Jassim Al-Thani, and the director of Egypt’s General Intelligence Service, Maj. Gen. Hassan Rashad, have been the top officials representing their countries in the negotiations.

• David Barnea, the chief of Israel’s foreign intelligence service, Mossad, is one of Israel’s main negotiators, alongside Ronen Bar, the head of the Shin Bet, a domestic security service, and Maj. Gen. Nitzan Alon of the Israeli military. Ophir Falk, a foreign policy adviser to Prime Minister Benjamin Netanyahu, has also participated in important meetings related to the negotiations.

• Khalil al-Hayya, a senior Hamas official based in Doha, is the militant group’s chief negotiator and has interfaced with Qatari and Egyptian officials about the details of a possible agreement.

• The United States has used its leverage to encourage Israel and Hamas to sign on to a deal. Bill Burns, the C.I.A. director, and Brett McGurk, a senior White House official, have crisscrossed the Middle East, pressing for a breakthrough in the talks. Steve Witkoff, Mr. Trump’s Middle East envoy, has also made trips to Qatar and Israel, meeting with top officials there.

What are they negotiating?

Israeli officials hope to secure the release of at least some of the roughly 100 hostages who have been held in Gaza since the Hamas-led attack on southern Israel on Oct. 7, 2023, that ignited the ensuing war in the territory.

Hamas leaders want to achieve an end to the war in Gaza, which has severely weakened the group’s armed wing and government, led to the displacement of nearly two million people, and reduced cities to rubble. Hamas officials have also said they are seeking a complete Israeli withdrawal from Gaza, the return of displaced people in the south of the enclave to the north, and the entry of materials for reconstruction.

What are the biggest obstacles?

• A major obstacle to the success of the talks has been the permanency of a cease-fire. While Hamas has demanded a comprehensive end to the war, Mr. Netanyahu has said he wants a “partial” deal that will allow Israel to resume the war after freeing hostages.

• Israel has been demanding vague language in the text of an agreement that leaves room for a resumption of fighting at some point, according to a Palestinian familiar with the matter and two Israeli officials. Mr. Netanyahu has feared that his right-wing coalition partners could take down his government and jeopardize his political future if he agrees to a deal that ends the war in Gaza, analysts say.

• Hamas has not suggested it would be willing to compromise on its demand to end the war. Last week, Osama Hamdan, a senior Hamas official, told a gathering in Algeria that there must be “an absolute end to the aggression.”

When Donald J. Trump was last president of the United States, the wealthy monarchies of the Persian Gulf had a mostly harmonious relationship with his administration. As Mr. Trump prepares to return to the White House, the leaders of those Gulf countries have generally welcomed him back.

But this time around, the Gulf states and Mr. Trump appear to be diverging on several cornerstone issues, like Israel and Iran. Differences over energy policies could also be a source of friction.

It is unlikely that there will be major tensions or ruptures with U.S. allies in the Gulf. But Mr. Trump will be encountering a region that has seen drastic shifts since Israel launched its war on Gaza in response to the Hamas-led attack of Oct. 7, 2023, in which the Israeli authorities say about 1,200 people were killed and about 250 taken hostage.

The war in Gaza, in which at least 45,000 people have been killed, according to health officials in the enclave, has rippled across the region. In Lebanon, the Iran-backed militant group Hezbollah has been battered by more than a year of fighting against Israel. And in Syria, rebels toppled the regime of Bashar al-Assad.

Now, while Mr. Trump is filling his cabinet with Iran hawks and staunch defenders of Israel, Gulf leaders have publicly been urging a softer stance on Iran and a tougher line on Israel.

They have also been calling on the United States to stay engaged with the region.

For now, the Trump administration has appeared eager to engage with the Gulf powerhouses of Saudi Arabia, Qatar and the United Arab Emirates.

In December, Mr. Trump’s pick as his envoy to the Middle East, Steve Witkoff, was in the Emirati capital, Abu Dhabi, where he attended a Bitcoin conference along with Eric Trump, the president-elect’s son. He also went to Riyadh, Saudi Arabia, where he met with Crown Prince Mohammed bin Salman, Axios reported.

Here’s a closer look at the issues facing Mr. Trump as he navigates an evolving relationship with his traditional Gulf allies.

Engagement in the Mideast

One of the clearest calls in the Gulf for Mr. Trump to avoid an isolationist agenda came from Prince Turki al-Faisal, the former head of Saudi Arabia’s intelligence services.

In an open letter to the U.S. president-elect published in November in The National, an Abu Dhabi-based newspaper, Prince Turki referred to an assassination attempt against Mr. Trump and expressed his belief that “God spared your life” in part so Mr. Trump could continue the work he had started in the Middle East during his first term. That mission was to bring “PEACE, with capital letters,” he wrote.

During his first term, Mr. Trump’s administration brokered the Abraham Accords that saw several Arab countries establishing ties with Israel.

A similar message to Prince Turki’s was delivered a few days later by Anwar Gargash, an adviser to Sheikh Mohammed bin Zayed, the U.A.E. president, at a conference in Abu Dhabi.

With the Gulf surrounded by an increasingly turbulent region, Mr. Gargash said, American leadership and partnership remained essential. “We need robust leadership that balances humanitarian concerns with strategic interests,” he said.

Going Harder on Israel

On Israel, the most striking shift in messaging in the Gulf has come from the de facto leader of Saudi Arabia, the crown prince. Speaking at an Arab League summit in Riyadh recently, Prince Mohammed for the first time called the Israeli military campaign in Gaza a “genocide.”

Just before the war in Gaza erupted in October 2023, Saudi Arabia appeared to be on the verge of forging diplomatic relations with Israel without fulfilling its longstanding precondition for doing so — the establishment of a Palestinian state. Such a deal would have reshaped the Middle East.

Under one plan, Saudi Arabia would normalize relations with Israel in exchange for stronger defense ties with the United States and American support for a civilian nuclear program in Saudi Arabia.

But recent statements by Prince Mohammed suggest that any deals are a long way off.

In addition to his statement referring to genocide in Gaza, he has also made it clear that Saudi Arabia will not establish diplomatic relations with Israel until a Palestinian state is created. That is still a distant prospect given strong opposition to such a state within the government of Prime Minister Benjamin Netanyahu of Israel.

“I think that the crown prince wanted to make his position clear and beyond any shadow of a doubt,” said Ali Shihabi, a Saudi businessman who is close to the kingdom’s ruling family.

The United Arab Emirates — a signatory to the Abraham Accords — has also signaled a hardened stance toward Israel.

The U.A.E. foreign minister, Sheikh Abdullah bin Zayed, told his Israeli counterpart last week that the Emirates would “spare no effort supporting Palestinians.”

Despite Saudi Arabia’s public stance on the status of a normalization deal, U.S. diplomats have indicated that the kingdom may be privately open to advancing one under a second Trump presidency — contingent upon a permanent cease-fire in Gaza and a tangible commitment by Israel toward a path to Palestinian statehood.

“All of that is ready to go if the opportunity presents itself with a cease-fire in Gaza as well as understandings on a pathway forward for the Palestinians,” the departing U.S. secretary of state, Antony J. Blinken, said on Wednesday. “So, there’s tremendous opportunity there.”

Détente With Iran?

During Mr. Trump’s first term, both Saudi Arabia and the United Arab Emirates championed his administration’s hawkish stance on Iran, seeing Tehran as a dangerous rival in the region.

They cheered when Mr. Trump withdrew the United States from a nuclear deal with Iran and hailed his decision to authorize the assassination of Qassim Suleimani, the general who directed Iran’s militias and proxy forces around the Middle East, in January 2020.

But the dynamics of the region have changed since Mr. Trump’s first term.

Saudi Arabia and Iran reached an accord in March 2023 that reduced tensions in the Persian Gulf and opened the door to high-level diplomatic contacts.

Bahrain, after years of tension with Iran, has made overtures to the Iranian government, with King Hamad bin Isa al-Khalifa saying there was “no reason to delay” the resumption of diplomatic relations. The tiny island kingdom also condemned Israel’s targeting of Iran last October, when a shadow war between the two countries broke out into the open with tit-for-tat attacks.

For Saudi Arabia, the goal is clear: to create a stable regional environment conducive to Prince Mohammed’s dream of diversifying the oil-dependent Saudi economy. For Iran, decades of economic and political isolation, compounded by rising domestic unrest, have made reconciliation with Riyadh a necessity.

There are also indications that Iran might be open to negotiating with Mr. Trump. Many former officials, pundits and newspaper editorials in Iran have openly called for the government to engage with Mr. Trump.

So far, Mr. Trump, too, appears open at least in charting a different course from the “maximum pressure” campaign of his first term. In November, Elon Musk, a close adviser to Mr. Trump, met with Iran’s ambassador to the United Nations, Iranian officials said.

“We have to make a deal because the consequences are impossible,” Mr. Trump said in September, referring to the threat of Iran’s pursuing nuclear weapons.

Possible Frictions Over Oil

While the Gulf Cooperation Council countries — Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates — appear open to Mr. Trump’s transactional approach to diplomacy, they could find themselves at odds with his economic policies.

A central promise of his campaign was to bolster U.S. oil and gas production, a move that could hurt Gulf economies.

If the United States increases oil production, as Mr. Trump has pledged, producers in the Gulf would have less scope to raise output without prompting a price drop.

“Increased U.S. oil exploration and production will lower prices and jeopardize the oil-driven economies of the Gulf,” Bader al-Saif, an associate fellow at the London-based research institute Chatham House, said in a recent report.

Mr. Trump is also expected to accelerate liquefied natural gas projects, reversing President Biden’s freeze on permits and increasing U.S. exports, particularly to Europe.

Qatar, one of the largest producers of the gas alongside the United States, would most likely be most affected, but it has so far played down its concerns.

Five months after Ukrainian forces swept across the border in the first ground invasion of Russia since World War II, the two armies are engaged in some of the most furious clashes of the war there, fighting over land and leverage in the conflict.

The intensity of the battles recalls some of the worst sieges of eastern Ukraine over the past three years, including in towns like Bakhmut and Avdiivka, names that now evoke memories of mass slaughter for soldiers on both sides.

The fighting, in the Kursk region of Russia, has taken on a layer of significance for the territory’s potential to play a role in any cease-fire negotiations. Facing the prospect of an unpredictable new U.S. president — who has vowed to end the war swiftly, without clarifying the terms — Ukraine hopes to use Russian territory as a bargaining chip.

Russia, relying on North Korean reinforcements, hopes to knock that territory out of Ukraine’s grasp.

“Here, the Russians need to take this territory at any cost, and are pouring all their strength into it, while we are giving everything we have to hold it,” said Sgt. Oleksandr, 46, a leader of a Ukrainian infantry platoon. “We’re holding on, destroying, destroying, destroying — so much that it’s hard to even comprehend.”

He and other soldiers, asking to be identified by only a first name or call sign in accordance with military protocol, said that waves of attacking North Korean infantry had made the battles far more ferocious than before.

“The situation worsened significantly when the North Koreans started arriving,” said Jr. Sgt. Oleksii, 30, a platoon leader. “They are pressuring our fronts en masse, finding weak points and breaking through them.”

Russia, with the help of an estimated 12,000 North Koreans, has retaken about half of the territory it lost over the summer. Its assaults over the past week have further eaten into the territory held by Ukraine.

But Ukrainian forces have also gone on the attack in recent days, seeking to secure an area west of Sudzha, a small town in Russia about six miles from the border that has become the anchor for Ukrainian forces, which seized about 200 square miles in August.

“If they keep pressing us and we don’t push back, the enemy will feel a sense of superiority,” said Andrii, 44, a military intelligence officer. “When someone keeps hitting you, and you don’t hit back, the attacker will feel psychologically comfortable, even relaxed.”

The Russians have largely thwarted the assault, but fighting goes on and the situation remains unpredictable, soldiers said.

The intensity of the battles could be glimpsed on the road approaching the Russian border: A steady stream of tanks, armored personnel carriers and other vehicles rolled past broken down and blown-up equipment.

Russian bombs and rockets exploded with thunderous force in border villages, and Ukrainian missiles could be seen streaking across the sky in the opposite direction.

Tens of thousands of drones hunted targets, too. They have transformed the battlefield, although Ukraine has improved its electronic warfare abilities, limiting the effectiveness of drones that rely on radio signals. Russia has now flooded the theater with drones guided by ultrathin fiber-optic cables, with a flying range of more than 10 miles.

The best current defense against them is a shotgun, Ukrainian soldiers said.

The renewed fighting comes against a deeply uncertain political backdrop. The U.S. president-elect, Donald J. Trump, spent months on the campaign trail questioning American military assistance to Ukraine. He has said he wants to bring the war to a swift end, but has not indicated how.

Russian forces have been on the offensive for more than a year in eastern Ukraine, making steady advances despite staggering losses.

With its incursion, Ukraine aims to create a buffer zone to protect hundreds of thousands of civilians in the city of Sumy, less than 20 miles from the border with Russia. Ukraine also wants to ease pressure on the eastern front by drawing Russians back onto their own land.

President Volodymyr Zelensky said the campaign had sent a powerful message to the world that Ukraine can do more than play defense.

“It’s one of our wins, I think one of the biggest wins, not just last year, but throughout the war,” Mr. Zelensky said on Thursday in Germany, while meeting representatives of nations providing military support to Ukraine.

Still, some military analysts have cautioned that Ukraine’s Kursk campaign could leave its forces increasingly stretched and losing ground in its own eastern Donbas region.

Many soldiers fighting in Kursk believe that the painful losses in eastern Ukraine would have been even worse without their campaign.

“We have to understand the Russians use their most elite soldiers and best reserves in this area,” said Capt. Oleksandr Shyrshyn, 30, a battalion commander in the 47th Mechanized Brigade. “Considering what they could be doing in other parts of Ukraine, it is good.”

He was still bleary-eyed after a battle, a few days earlier, to thwart a large Russian assault.

The Russians attacked Ukrainian positions in six waves, employing more than 50 tanks, armored personnel carriers and other vehicles.

While dozens of enemy soldiers were killed and injured and a large amount of the Russian equipment destroyed, Captain Shyrshyn said, the Russians advanced a couple of miles.

“When the first wave comes, we focus on it, deal with it, and then the next one comes,” he said. There is no time to redirect artillery or other resources as the next wave moves in from a different line of attack.

“We fall behind,” he said. “Then the next wave comes, and one of them manages to reach the required section and accomplish its task.”

It remains difficult, he said, to see how so many in the West view the war in Ukraine like a video game and refuse to see the threat Russia poses to the world.

He acknowledged the decline in Ukrainian morale over nearly three years of war, but said most soldiers still understood why they must fight. “Stopping will mean our death, that’s all,” he said.

North Korea’s entry into the war, some Ukrainian soldiers said, should alarm European nations and their allies.

The North Korean troops have fought as a disciplined, dedicated and fearless force, they said, typically moving in large formations on foot, even through minefields while under heavy artillery fire and being stalked by drones. The Ukrainian authorities on Saturday said that their forces captured two North Korean soldiers and that they were the first to be taken alive so far.

Sgt. Oleksandr, the platoon leader, said the carnage in Kursk was as terrifying as anything he had witnessed since joining the army in 2014.

“You look and can’t fully grasp where you are, seeing every day how many people we destroy,” he said.

He compared it with Bakhmut, when machine gunners had to be regularly replaced because they could not handle the pace of killing. “After two hours of laying down so many people, they couldn’t take it mentally,” he said.

“It’s the same here now,” he said, sharing a cellphone video showing the aftermath of a recent assault. The field was littered with bodies, torn and twisted and piled in ways that made it hard to count the dead.

“The worst is for the infantry,” he said. “When you’re sitting there, and they’re coming at you, and everything is flying at you.”

Anastasia Kuznietsova contributed reporting.