He demanded the release of a convicted criminal and far-right agitator. He falsely accused the prime minister, Keir Starmer, of failing to go after child rapists when he was head of public prosecutions. He endorsed a post calling on King Charles III to dissolve Parliament and call elections to remove Britain’s seven-month-old Labour government, a constitutional impossibility.

Elon Musk has once again set his sights on Britain, putting the country in the bull’s-eye in the capricious world of his online obsessions. In a fusillade of posts that began before the new year, Mr. Musk moved on from his enthusiastic boosting of a far-right party in Germany to targeting Britain on multiple politically sensitive fronts.

After mostly ignoring Mr. Musk’s trolling, which has been going on for months, the British government on Friday snapped back, though in characteristically polite fashion.

“Elon Musk is an American citizen and perhaps ought to focus on issues on the other side of the Atlantic,” the government’s health minister, Andrew Gwynne, said in an interview with LBC radio. Mr. Gwynne’s boss, the health secretary, Wes Streeting, told reporters, “Some of the criticisms Elon Musk has made, I think, are misjudged and certainly misinformed.”

Britain is one of several European countries where Mr. Musk is trying to replicate the influence he wielded on behalf of President-elect Donald J. Trump in the American election last fall. In addition to Germany, where his advocacy of a far-right party with neo-Nazi ties, Alternative for Germany, has roiled that country’s politics before elections next month, Mr. Musk has nurtured close ties to Italy’s right-wing prime minister, Giorgia Meloni.

In Britain, Mr. Musk’s antagonism toward the Labour government is rooted in part in its aggressive response to hate speech online. Officials said false and inflammatory posts helped incite anti-immigrant riots that followed the killing of three girls in a mass stabbing in the town of Southport last July. They arrested more than 30 people, which prompted Mr. Musk to condemn the government for what he called an attack on the free speech that he extols on his platform, X.

Britain, he said, “is turning into a police state.”

Since then, however, Mr. Musk has waded into other volatile issues, from declaring his support for the anti-immigrant party, Reform U.K., to stirring up anger over the government’s response to a decade-old child sexual abuse scandal in the northern town of Rotherham. An estimated 1,400 girls were exploited by “grooming gangs” composed largely of British Pakistani men.

Perhaps most provocatively, Mr. Musk has taken up the cause of Tommy Robinson, a far-right, anti-immigrant agitator whose real name is Stephen Yaxley-Lennon. He has been in prison since October after being convicted of defying a court order by repeating false claims about a teenage Syrian refugee who had successfully sued him for libel.

Mr. Robinson has been previously jailed for assault, mortgage fraud and traveling on a false passport to the United States, where he has sought to establish ties with right-wing groups.

“Free Tommy Robinson!” Mr. Musk posted on Jan. 2 as his pinned item atop his X account, which has 210 million followers.

Mr. Musk’s championing of Mr. Robinson has put his other right-wing allies in Britain in an awkward spot. Nigel Farage, the leader of Reform U.K. and a close ally of Mr. Trump’s, has long shunned Mr. Robinson, who founded the English Defence League, an Islamophobic, nationalist group known for its violent street protests in the late 2000s and 2010s.

Mr. Farage, who has reveled in Mr. Musk’s endorsement and has courted him in the hopes of winning a donation to Reform U.K., echoed his demands for a new investigation of the child sex abuse scandal. But he has been conspicuously silent about Mr. Robinson.

As in Germany, where Mr. Musk’s promotion of the far-right AfD party provoked a widespread backlash against him, Mr. Musk’s interventions have won him few fans in Britain. But analysts say his proximity to, and influence over, Mr. Trump mean that his opinions, amplified by his social media platform, cannot be ignored by the government.

“His message doesn’t work in Britain and Germany, and yet the governments are constrained by their relationships with Trump,” said Sunder Katwala, the director of British Future, a research organization in London. “It will be hard enough to have a relationship with Trump. What Musk does is put this nongovernment official in the center of the court.”

Mr. Katwala argued that it made sense for the government to respond to Mr. Musk’s more extreme or erroneous statements, if only because his unpopularity makes him an inviting target for other critics. “They leave an open goal by not saying anything,” he said.

Privately, British officials say they hope that after Mr. Trump’s inauguration later this month, Mr. Musk will be too busy overhauling the American federal government to continue his daily barrage of criticism of Britain and Germany. But in the meantime, his online reach is broad enough that “it affects the political weather,” Mr. Katwala said, citing the child sex abuse scandal as a case in point.

Mr. Musk’s posts have helped whip up a tempest over a case that was the subject of local and national inquiries dating back to 2014. After one of Mr. Starmer’s ministers, Jess Phillips, pushed back on calls for yet another national investigation — saying it was a matter for the local council — the leader of the opposition Conservative Party, Kemi Badenoch, followed Mr. Farage in castigating the government. “No one in authority has joined the dots,” she posted on X on Jan. 2.

On Friday, Mr. Musk claimed that Ms. Phillips, the under secretary for safeguarding and violence against women and girls who has long campaigned for women’s rights, was a “rape genocide apologist” — language that women’s rights supporters said jeopardized Ms. Phillips’ safety. He has also tried to turn the scandal against Mr. Starmer, who ran the Crown Prosecution Service from 2008 to 2013, when the abuses first came to light.

Although several men were imprisoned, the inquiries found that the police and prosecutors were slow to react to the allegations, in part because the victims were reluctant to come forward and in part because of worries about racism, given that most of the accused were British Pakistanis.

“Starmer was complicit in the RAPE OF BRITAIN when he was head of Crown Prosecution for 6 years,” Mr. Musk said in a post that was pinned to the top of his account earlier on Friday. “Starmer must go and he must face charges for his complicity in the worst mass crime in the history of Britain.”

In fact, in 2013, in the wake of the scandal, Mr. Starmer published new guidelines for how the Crown Prosecution Service should deal with cases of sexual exploitation of children.

Having won a landslide Parliamentary majority in July, Mr. Starmer is in no immediate danger of losing his job. But the drumbeat of disinformation and criticism from Mr. Musk, combined with the prospect of him giving money to Reform U.K., has rattled people across the political spectrum in Britain. Lawmakers have called on the government to tighten laws to restrict foreigners from donating to British political parties.

Mr. Musk’s endorsement of posts calling on Charles to step in and call an election betrayed his ignorance of how Britain works. Under the terms of its constitutional monarchy, the king can dissolve Parliament, but only at the request of the prime minister, who decides when to call an election.

“He’s a 21st-century Citizen Kane,” Mr. Katwala said of Mr. Musk. “He’s got a picture of Britain, a picture of Germany, and he looks for information that confirms those pictures. The problem he has in exporting it to Britain or Germany is the evident lack of knowledge of Britain or Germany.”

When around 100 criminal investigators and police officers entered a hilly compound in central Seoul on Friday morning, they tried to achieve something that has never been done before in South Korea: detain a sitting president.

First, they made it through two blockades formed by parked vehicles and people. Then, when they came within 650 feet of the building where President Yoon Suk Yeol was believed to be holed up, they came face to face with an even more formidable barrier: 10 buses and cars along with 200 elite soldiers and bodyguards belonging to Mr. Yoon’s Presidential Security Service. Small scuffles erupted as the investigators tried in vain to break through and serve a court-issued warrant to take Mr. Yoon away.

Three prosecutors were allowed to approach the building. But there, Mr. Yoon’s lawyers told them that they could not serve the warrant because it was “illegally” issued, according to officials who briefed news media about what happened inside the compound.

Outnumbered, the 100 officials retreated after a five-and-a-half-hour standoff.

“It’s deeply regrettable,” the Corruption Investigation Office for High-Ranking Officials, the independent government agency that led the raid into the presidential compound on Friday, said in a statement. It accused Mr. Yoon — who has already been suspended from office after being impeached by Parliament last month — of refusing to honor a court-issued warrant. “We will discuss what our next step should be.”

The failure to bring in the deeply unpopular president deepened a growing sense of helplessness among South Koreans, exacerbated by the country’s sharply polarized politics. The nation appears rudderless and distracted by infighting at a time when it faces major challenges at home and on the international scene.

There is already uncertainty around its alliance with the United States as the unpredictable Donald J. Trump prepares to return to the White House. Seoul’s decades-old foe North Korea has sought to score propaganda points from the South’s political quagmire, with its state media reporting that its neighbor was in “paralysis of its state administration and spiraling sociopolitical confusion.”

And, at home, the crash of a Jeju Air passenger jet that killed 179 of the 181 people on board on Sunday has added to as list of challenges that range from widespread labor strikes to rising household debts. On Thursday, the finance ministry sharply downgraded its growth forecast for 2025.

A Constitutional Court is deliberating whether to remove Mr. Yoon, who was impeached on Dec. 14 by the National Assembly. That came after he abruptly declared martial law 11 days earlier, prompting national outrage and calls for his ouster.

On Friday, the besieged Mr. Yoon vowed to fight to return to office through the Constitutional Court trial and showed he had no intention of voluntarily subjecting himself to criminal investigations. Mr. Yoon faces accusations that he committed insurrection by sending armed troops into the National Assembly during his short-lived military rule.

By refusing to honor the warrant, Mr. Yoon “kept adding more reasons he should be removed from office through impeachment,” said Lim Ji-bong, a professor of law at Sogang University in Seoul.

“He may think he survived today, but what he did today would not go down very well with the justices at the Constitutional Court and judges who would eventually try his insurrection case.”

Mr. Yoon is not the first South Korean politician who has defied court warrants to detain them. In 1995, prosecutors wanted to question the former military dictator Chun Doo-hwan on insurrection and mutiny charges stemming from his role in a 1979 coup and a massacre of demonstrators the following year. He defied the summons and headed to his southern hometown, trailed by a crowd of supporters.

The prosecutors chased him there. After an overnight standoff, Mr. Chun surrendered himself.

But unlike Mr. Yoon, Mr. Chun was out of office when he faced the insurrection charge. Mr. Yoon, though suspended, is still guarded with the full support of his Presidential Security Service, a government agency that hires teams of elite bodyguards and anti-terrorist experts selected from the police, military and other government services.

“People who have seen him rely on his bodyguards as a shield against his legal trouble will see him as a coward,” Mr. Lim said.

The investigators warned that they would charge the presidential bodyguards with obstruction of justice.

“We will do everything we can to provide security for the object of our service according to laws and principles,” the Presidential Security Service said in a statement.

Public surveys showed that a majority of South Koreans wanted Mr. Yoon ousted and punished for insurrection. But his governing party, which opposed his impeachment, denounced attempts to hold him.

Mr. Yoon also has die-hard supporters — mostly among mostly older South Koreans. Thousands of his supporters have been camped out for days on the pavement, chanting, “Let’s protect Yoon Suk Yeol!”

In a message delivered on New Year’s Day, Mr. Yoon called them “citizens who love freedom and democracy” and thanked them for braving the cold weather to show their support out on the street near his home.

“I will fight with you to the end to save this country,” Mr. Yoon said.

When the officials withdrew from Mr. Yoon’s compound, they shouted: “We have won!”

Protesters who have been clamoring for Mr. Yoon’s arrest began gathering again on Friday, marching near Mr. Yoon’s residence and shouting “Arrest Yoon Suk Yeol!” They, as well as the country’s opposition parties, expressed fury over the failure to detain Mr. Yoon, calling his presidential security service “accomplices” in an insurrection.

“I’m so angry,” said Lee Ye-seul, 19, a university student in Seoul. “I will speak out until he is removed and the people involved in the insurrection are punished.”

To Mr. Yoon’s supporters outside his residence, the security service was the last line of defense to save Mr. Yoon.

“The presidential guard should throw grenades if necessary to stop them from coming near the president,” said Lee Young-jin, 65.

But Mr. Yoon’s tactic of stoking political divides to avoid his legal trouble reflected poorly on South Korea, said Ahn Byong-jin, a professor of political science at Kyung Hee University in Seoul.

It “exposed weaknesses in South Korea as a democracy,” he said.