The amount of humanitarian aid entering Gaza surged dramatically on Sunday, with more than 630 trucks entering the impoverished and hungry enclave on the first day of the cease-fire, according to United Nations officials — the highest figure since the start of the war more than 15 months ago.

The truce allowed the U.N. World Food Program to “bring in urgently needed food aid at scale and begin pulling the war-ravaged territory back from starvation,” the agency said in a statement on Sunday. Tom Fletcher, the U.N. relief chief, said in a statement on Monday that more than 300 of the trucks went to northern Gaza, where aid had been the most scarce and humanitarian officials have warned of a possible famine.

During the war, fewer than 100 trucks per day had been entering the enclave, and deliveries had at times been suspended. Relief agencies accused Israel of overly restricting deliveries with stringent inspections and the closure of border crossings, which Israel denied, and have said that at least 200 trucks per day were required to provide food, medicines, fuel, clean water and other essentials.

With the cease-fire between Israel and Hamas taking effect, aid convoys seemed to enter Gaza without issues, and no attempts at stealing or looting the aid were reported on Sunday or Monday, according to Juliette Touma, a spokeswoman for the main U.N. agency that assists Palestinians. She added that local police officers were present in some parts of Gaza to secure the convoys, while in other areas security was not needed.

Uniformed police officers and armed fighters, rarely seen in the open during the war, were visible in cities and towns across Gaza after the cease-fire took effect. It was an apparent show by Hamas, which had controlled the enclave for years, that it is still in charge and plans to hold onto power.

Videos posted to social media showed convoys driving through Gaza on Sunday, as people gathered calmly on roadsides, refraining from approaching the trucks. It was a stark contrast to the apocalyptic scenes of wartime aid deliveries, when desperate crowds swarmed and climbed onto the trucks in hopes of securing a food package or bag of flour, sometimes resulting in violence.

“What was very noticeable is that none of the trucks that entered yesterday were looted,” said Nebal Farsakh, a spokeswoman for the Palestinian Red Crescent. “And this was the first time in 15 months that this many trucks entered Gaza,” she added.

What was less clear was how efficiently and equitably aid was being distributed after it entered Gaza, and some residents said they have yet to receive or even see the aid. Ms. Touma said that UNRWA staff and aid workers from other agencies were still sorting through the aid that has come in since Sunday before it is eventually delivered to people.

“It’s the second day of the cease-fire and they said that aid and flour have come in but unfortunately we haven’t seen any of it yet,” said Moustafa al-Aloul, a 22-year-old from northern Gaza. “Currently, the markets literally have nothing,” he added.

The Gazan ministry of social development, a part of the Hamas-led administration, said in a statement on Monday that it had “made all preparations to receive aid” and will provide all the permits needed for aid organizations to receive and distribute the aid. “Work will be done in a coordinated manner between all partners to ensure the fair distribution of aid to all citizens,” the ministry said, adding that aid will be provided to families inside and outside shelter centers and tent encampments.

Israeli officials have accused Hamas of hoarding essential supplies to serve its own members and to wield control over the population, and there have been reports of profiteers seizing aid and then selling it on the black market. Aid officials say the solution is to end the scarcity.

Ms. Touma said the convoys entering Gaza have included some trucks carrying commercial goods for sale, which have rarely reached Gaza during the war.

“There were several goods that people take for granted that were very much missing from the market,” Ms. Touma said in an interview on Monday. “So it’s very good that commercial supplies have also come in because you can’t turn the two million people in Gaza into a nation that is solely dependent on aid,” she added.

The World Food Program said that on Sunday it delivered ready-to-eat meals and bags of wheat flour. It aims to send at least 150 truckloads of food into Gaza every day, along with other supplies, as well as restocking bakeries and providing nutritional supplements for children facing malnutrition.

Ameera Harouda contributed reporting from Qatar, Matthew Mpoke Bigg from London and Vivian Yee from Cairo.

At least 80 people are dead and more than 11,000 have been forced to flee their homes in Colombia, officials say, amid fierce clashes between two rival armed groups on the border with Venezuela.

The violence, in a northeast region called Catatumbo, is some of the worst the country has suffered through in recent years, raising concerns that the country is moving in the opposite direction of “total peace” — a goal made a priority by the country’s leftist president, Gustavo Petro, who is more than halfway through his four-year term.

The Colombian leader visited the region on Friday, writing on X that his government “stands with the people of Catatumbo.” He has also sent troops and humanitarian assistance.

Displaced families are taking refuge in a stadium in Cúcuta, a border town better known in recent years for receiving Venezuelan migrants. In some places, Colombians are fleeing into Venezuela — home to its own humanitarian crisis — and the Venezuelan autocratic leader there, Nicolás Maduro, has promised to send them aid.

The clashes in Catatumbo are a stark departure from the hope that swept across parts of Colombia less than a decade ago, when the country signed a peace deal with its largest rebel group, the Revolutionary Armed Forces of Colombia, or FARC.

The nation had suffered through decades of internal conflict, with left-wing guerrilla groups, including the FARC; paramilitary organizations; and the government fighting for control of the country and for lucrative industries like narcotrafficking.

Thousands of FARC fighters laid down their arms in the 2016 agreement, and at the time it felt like a seismic moment for one of the world’s most violent countries. But old rebel groups, including the National Liberation Army, or ELN, persisted, while new ones emerged, all fighting for control of territory and industry left behind by the FARC.

In some cases, these new groups consist of former FARC fighters, and they have divided and subdivided, helping fuel an ever more complicated conflict.

Most of the violence has played out in rural parts of the country with many Colombians living in cities only dimly aware of the violence that has been unfolding not far from their homes.

In past, the FARC fought the government, seeking to topple and replace it. Today’s armed groups are more focused on fighting each other, battling over land and profits, with the military trying to contain them.

Catatumbo is home to vast fields of coca, the plant that is a base product in cocaine. Two groups control the territory, the ELN and a group of former FARC members called the 33rd Front, said General Luis Emilio Cardozo, the head of the Colombian army, speaking to reporters over the weekend.

A precarious peace between the two groups broke down last week. General Cardozo said there had been four or five clashes between the groups in recent days, and in other cases armed fighters were going door-to-door, targeting former FARC fighters they suspected of being part of the 33rd Front.

“It was a very well planned criminal operation,” he said, “they went with a list in hand looking for the people they wanted to kill.”

In a message posted on X on Sunday, the ELN called the 33rd Front the “only objective of our actions.”

But many victims, including those fleeing their homes, appear to be civilians.

In response to the violence, Mr. Petro has suspended ongoing peace talks with the ELN.

With the military distracted, a separate conflict broke out in recent days between two former FARC groups in Guaviare, a department in the south-central part of Colombia, according to the country’s ombudsman’s office.

Organizations including the International Crisis Group have warned for years that the country’s security situation has deteriorated since 2016, and could erupt into violence at any moment.

“We are very concerned that moment is now,” said Elizabeth Dickinson, a Colombia-based analyst for the nonprofit organization. “Escalations on various front lines have taken the conflict to a very dangerous inflection point.”

Ms. Dickinson called the scale of conflict in Guaviare “very significant,” and said it had the potential to spread across several departments in southern Colombia. She added that there are “many children” in the ranks of the armed groups in that region.

The clashes in Catatumbo, in the north, on the border with Venezuela, come amid growing tensions between Mr. Petro and Mr. Maduro, who has provided safe haven to members of the ELN.

Both Mr. Petro and Mr. Maduro call themselves leftists, and just two years ago, the two were shaking hands in Caracas and promising more productive relations.

But Mr. Petro has turned more critical of the autocrat in recent weeks, reprimanding him for locking up political opponents and refusing to release the results of a recent presidential vote that Mr. Maduro claimed to win, but that many countries agree was actually won by a top opposition leader.

This has provoked the ire of Mr. Maduro, who has accused Mr. Petro and other leaders in meddling in Venezuela’s internal affairs.

The International Committee of the Red Cross said last year that it was tracking eight different armed conflicts inside Colombia.

On Sunday night the country’s ombudsman, Iris Marin, said 11,000 people had been displaced in Catutumbo in just four days, including many children. William Villamizar, the governor of North Santander, a border department, said the death toll had risen to more than 80 people.

Ms. Marin said that the violence amounted to “one of the largest and most serious humanitarian crises that Catatumbo has faced, if not the worst.”

She blamed the conflict on a “few people” in the region and called on them to end it. “Those few people have the ability to stop the suffering.”

Federico Rios contributed reporting.

For the second time in less than decade, Mexico is preparing to negotiate with President-elect Donald J. Trump, who is threatening the neighboring country with sky-high tariffs, mass deportations and military strikes on cartels.

The stakes are huge for Mexico’s 130 million people. Among major economies, Mexico is exceptionally dependent on the United States, sending about 80 percent of its exports to the American market.

Mexico’s top negotiators are adopting an assertive stance to negotiating with Mr. Trump this time around. Some of them can draw from experience dealing with the first Trump administration: Mexico’s populist president at the time, Andrés Manuel López Obrador, forged a warm relationship with Mr. Trump, and Mexico avoided steep tariffs while acceding to demands to curb migration.

“We will find a solution because we have structural advantages,” Marcelo Ebrard, the economy minister, said this month, listing factors like greater economic interdependence between the two countries and declines in fentanyl deaths and migration.

President Claudia Sheinbaum of Mexico has set the tone of this approach. While Mexico’s government has been unable to meet with the incoming Trump administration, she has blended conciliatory words for Mr. Trump with rhetorical pushback and vows that Mexico could hit back with retaliatory tariffs of its own.

“We coordinate, we collaborate, but we will never become subordinated,” Ms. Sheinbaum said in a speech this month.

At the same time, Ms. Sheinbaum’s government has already mobilized to respond to some of Mr. Trump’s concerns, expanding migration deterrence efforts and increasing seizures of illicit opioids.

The cornerstone of this strategy is a wager that the new administration in Washington needs Mexico, and its fast-expanding, low-cost industrial base, if the United States hopes to counter its largest rival: China.

Here are four factors informing Mexico’s preparations for dealing with the new Trump administration.

Mexico is increasingly important to the U.S. economy.

Mexico’s economic relationship with the United States has changed considerably since Mr. Trump was last in the White House, especially as a result of the coronavirus pandemic’s disruption of global supply chains.

Mexico eclipsed China in 2023 as the United States’ top trading partner in goods, as manufacturers shifted operations to Mexico to be closer to the American market.

Trade ties deepened even further last year, when Mexico displaced China to become the top source of imports for the United States and the top destination for American food exports.

“It’s an unprecedented level of interdependence,” said Diego Marroquín Bitar, a scholar who specializes in North American trade at the Wilson Center, a Washington research group.

Mexico’s government is showcasing these trade ties as it makes the case that imposing U.S. tariffs on Mexico could raise inflation and hurt American consumers.

But those deepened ties also leave Mexico with heightened vulnerabilities.

One may be remittances. Mexicans working in the United States sent home $63 billion in 2023, twice as much as when Mr. Trump took office eight years ago, and mass deportations could cause that figure to plummet.

Proposals to tax remittances, including a bill sponsored by Vice President-elect JD Vance, are also gaining momentum.

Migration flows and fentanyl deaths are falling.

While Mr. Trump has repeatedly raised alarms about migration from Mexico, illegal crossings along the U.S.-Mexico border are at their lowest level since the summer of 2020. Only about 46,000 people crossed the border illegally in November, the lowest number under President Biden.

The Biden administration’s restrictions on asylum for migrants contributed to this decline. But so did policies in Mexico, which has sought to dissuade migrants, largely from other Latin American countries, from reaching the U.S. border.

Mexico has broken up migrant caravans and expanded a shadowy busing program that has transported thousands of migrants from the country’s northern border to sites deep in its south.

Just in the last quarter of 2024, Mexico intensified this crackdown by detaining about 475,000 migrants, the authorities said, more than double the number held in the first nine months of the year. Most of these migrants are quickly released, allowing them to stay in Mexico; only a small fraction are deported to their home countries.

Another issue that Mr. Trump has cited frequently is the impact of illegal drugs, particularly fentanyl, flowing across the border. After surging to horrifying levels, overdose deaths from illegal drugs are also falling. They were down about 14.5 percent in the 12 months that ended in June 2024 from the same period a year earlier.

Experts say that expanded treatment, prevention and education efforts in the United States played a role in this decline. While more evidence is needed, U.S. efforts to crack down on chemical precursors from China and the Mexican cartels using these chemicals to make fentanyl also may be restricting supplies.

Ms. Sheinbaum has also begun targeting the fentanyl trade. Last month, Mexican security forces captured 20 million doses of the drug in the country’s largest synthetic opioid seizure.

Cartel violence is still rising over vast areas.

Neither declines in border crossings or fentanyl overdoses could much make a difference if Mr. Trump chooses to focus on the cartel bloodshed gripping large parts of Mexico as justification for imposing tariffs on its exports.

Clashes between rival cartel factions have recently turned the northwest state of Sinaloa into a war zone. Brutal political assassinations have cast a pall over Guerrero in southwest Mexico.

Turf battles in Guanajuato, a center for car manufacturing northwest of Mexico City, have been marked by one massacre after another in recent weeks.

During his previous term, and again while campaigning for his new term, Mr. Trump raised the possibility of taking military action against cartels as a way of limiting their smuggling of illicit drugs into the United States. A potential designation of these groups as “terrorist organizations” could open the way for such moves.

Mexico’s government has long viewed such a possibility as a nearly unthinkable violation of its sovereignty. But some former officials with previous experience negotiating with Mr. Trump warn that Mexico needs to take such threats seriously.

Ms. Sheinbaum highlighted last week the willingness of Marco Rubio, Mr. Trump’s pick for secretary of state, to collaborate on curbing cartel activities.

“We take him at his word,” Ms. Sheinbaum said of Mr. Rubio.

“Trump 2.0 is going to be a different Trump,” said Ildefonso Guajardo, a former economy minister who negotiated with the Trump administration in 2017 and 2018. “His team will be far less balanced in terms of trying to make him aware of the consequences of some decisions.”

And while fentanyl deaths are declining in the United States, the drug is still claiming tens of thousands of lives each year. The explosion of violence in Sinaloa highlights how the groups responsible for the fentanyl trade remain active and well armed.

A recent flood of imported Chinese cars into Mexico has increased tensions over the inroads that China is making into key industries in North America.

Mexico, which has a $105 billion trade deficit with China, moved quickly in recent weeks to assuage concerns that China could use its foothold in Mexico as a way to gain greater access to U.S. markets.

Mexico imposed tariffs viewed as targeting online Chinese retailers like Temu and Shein, then unveiled a new industrial policy last week aimed at reducing imports from China while bolstering supply chains to the United States.

With such measures, Mexico’s government is seeking to drive home its contention that the United States needs Mexico to confront the greater economic threat of China. But will that be enough for Mr. Trump?

If not, and if ties with Washington sour significantly, Mexico still has a kind of “nuclear option” involving strengthening its economic ties with China, according to Scott Morgenstern, a professor of political science at the University of Pittsburgh.

“Mexico could turn to Washington’s biggest economic rival at a time when Beijing is seeking to assert more influence across Latin America,” Mr. Morgenstern said.

The trial began on Monday for Axel Rudakubana, 18, who is accused of carrying out a knife attack at a dance class last July in the northern English town of Southport that left three children dead and 10 other people injured.

Mr. Rudakubana faces three charges of murder for the deaths of Bebe King, 6, Elsie Dot Stancombe, 7, and Alice da Silva Aguiar, 9, who were taking part in a Taylor Swift-themed dance and bracelet-making class during their summer break from school.

He is also charged with the attempted murder of 10 people, including eight other children and two adults, and with possession of a knife for the attack on July 29.

After the stabbings, the police searched Mr. Rudakubana’s house and said they found ricin, a lethal toxin, and a PDF file titled “Military Studies in the Jihad Against the Tyrants: The Al Qaeda Training Manual.” Mr. Rudakubana was subsequently charged with production of a biological toxin and with “possessing information of a kind likely to be useful to a person committing or preparing an act of terrorism.”

However, the authorities have not so far declared the episode an act of terrorism. Serena Kennedy, the chief constable of the Merseyside Police, which oversees policing in the region, said in a statement in October that “for a matter to be declared a terrorist incident, motivation would need to be established.” She added: “We would strongly advise caution against anyone speculating as to motivation in this case.”

Not-guilty pleas have been entered on Mr. Rudakubana’s behalf for all the charges. Throughout the legal proceedings so far, he has declined to speak.

The trial will take place at Liverpool Crown Court and is expected to last around four weeks.

Mr. Rudakubana was born in Cardiff, Wales, to parents who were originally from Rwanda. He was living in Banks, a village north of Southport, at the time of the attack.

Last week, Britain’s attorney general, Richard Hermer, issued an official advisory reminding social media users and journalists about the risks of contempt of court and warning that inaccurate or speculative commentary could influence the jury’s deliberations. Anything that asserts or assumes Mr. Rudakubana’s guilt could jeopardize the criminal trial, he warned.

After the Southport attack, Britain was convulsed by a series of violent riots, as disinformation about the attacker’s identity swirled on social media and messaging apps. False claims that the suspect was an undocumented immigrant or newly arrived asylum seeker were amplified by anti-immigration activists and members of the far right.

Several people, including a neo-Nazi, were later found to have helped coordinate outbreaks of unrest, which included attacks on mosques and hotels where asylum seekers were staying, and which led to dozens of police officers being injured.

Mr. Rudakubana was 17 at the time of the attack and, under English court rules, he would usually have retained his anonymity until he turned 18. But a few days after the attack, a judge took the unusual step of releasing his name in an attempt to combat the spread of misinformation.

Since the riots last summer, hundreds of people have been charged for their involvement in the violent disorder across the country, and dozens of people have been sentenced to prison time.

Yvette Cooper, Britain’s home secretary, said in a statement on Monday morning that the trial would be a “deeply traumatic and distressing time for the families of Alice, Bebe and Elsie, the survivors, and the people of Southport and the whole country.”

“The most important thing for all of us is to ensure that the legal process can take its course, to respect the difficult job the court has to do so there is a fair trial and justice can be done,” she added.