President Biden expressed concern on Friday about what he called “dangerous and destabilizing cooperation” between North Korea and Russia, as he met with the leaders of South Korea and Japan at the global summit of Asia Pacific leaders in Peru.

In a joint statement, Mr. Biden, Shigeru Ishiba, the prime minister of Japan, and President Yoon Suk Yeol of South Korea, said they “strongly condemn” the cooperation between North Korea and Russia, including the decision by North Korea to send thousands of troops to Russia to help President Vladimir V. Putin in his war with Ukraine.

“Deepening military cooperation between the DPRK and Russia, including munitions and ballistic missile transfers, is particularly egregious given Russia’s status as a Permanent Member of the U.N. Security Council,” the three leaders said, using an acronym for North Korea. “We remain resolute as ever in supporting Ukraine as it exercises its inherent right to self-defense as enshrined in Article 51 of the U.N. Charter.”

A senior American official, who spoke on condition of anonymity to describe the discussions during the 40-minute closed-door session, said that the issue of Russia-North Korea cooperation dominated the discussion between the three leaders.

The president and his aides have said in recent weeks that they are deeply worried about actions by Kim Jong Un, North Korea’s leader, including the dispatching of troops to Russia and new testing of a long-range ballistic missile.

On Tuesday, Mr. Biden said those developments must be countered by close coordination with allies in the region. Flanked by Mr. Ishiba and Mr. Yoon, Mr. Biden expressed confidence in new security and economic cooperation that the three nations announced during a summit last year at Camp David.

“I am proud to have helped be one of the parts of building this partnership,” Mr. Biden said. He did not mention the possible impact of President-elect Donald J. Trump’s return to the White House, but he noted that Friday’s meeting would be his last with the group.

“I think it’s built to last. That’s my hope and expectation,” Mr. Biden added.

Aides said Mr. Trump’s name did not come up during the meeting of the three leaders. The senior official said that the administration is focused on “the here and now” and is not dwelling on how Mr. Trump might undo what Mr. Biden and his aides have put into place during the last four years.

But his election has still loomed over Mr. Biden’s visit to Peru, his last major trip abroad to meet with world leaders before his term ends in January. The president is scheduled to leave Peru on Sunday for a brief stop in the Amazon rainforest before heading to Rio de Janeiro for a second summit of the Group of 20 nations.

Neither Mr. Biden nor his top national security officials have speculated over what parts of the president’s foreign policy approach will be discarded by Mr. Trump, who has embraced an “America First” philosophy and criticized nearly all of Mr. Biden’s approach to the world.

On Friday, Mr. Biden said only that “we’ve now reached a moment of significant political change.”

Jake Sullivan, the president’s national security adviser, told reporters aboard Air Force One on Thursday that officials in all three countries were prepared to work toward making the close cooperation between them an “enduring feature of American policy in the Indo-Pacific going forward.”

That will include the establishment of a “secretariat” to make the security and economic arrangements permanent. Mr. Sullivan said he expects that to have bipartisan support, adding: “We fully expect that it would continue under the next administration — though, of course, they’ll make their own decisions.”

Mr. Biden organized last year’s Camp David summit as a response to increasing North Korea aggression in the Asia Pacific region, among other issues. Since then, the rogue nation has added to those concerns by moving closer to Russia. Administration officials have said for months that they believe Mr. Kim has been supplying small arms and ammunition to Russia for use in the Ukraine war.

Last week, American and Ukrainian officials said thousands of North Korean troops had joined Russian soldiers for what is believed to be an assault in western Russia aimed at retaking territory seized by Ukraine in the Kursk region in recent months.

The addition of North Korean troops appears to have helped Mr. Putin as he prepares to mount the counteroffensive without having to shift any of his forces away from the fighting in the eastern parts of Ukraine. Officials have said they are also concerned that, in return, Russia may help North Korea improve its nuclear capabilities and missile technology.

“The possibility of a seventh nuclear test remains ever-present,” Mr. Sullivan told reporters. “It’s something we’re vigilant for. Transitions have historically been time periods when the DPRK has taken provocative actions, both before and after the transition from one president to a new president. So, that’s something we are watching very carefully and will be watching every day between now and January 20th.”

Iran sent a message to the Biden administration in October saying that it was not trying to kill Donald J. Trump, as Tehran attempted to ease rising tensions with Washington, according to U.S. officials, as well as an Iranian official and an analyst.

The message, sent to Washington through an intermediary, came after a note from the Biden administration in September that warned that the United States would consider any Iranian attempt on the life of Mr. Trump, then the Republican candidate for president, to be “an act of war.”

Since Mr. Trump won the Nov. 5 election, many Iranian former officials, pundits and media outlets have been publicly advocating for Tehran to try to engage with the president-elect and pursue a more conciliatory approach, despite vows from Mr. Trump’s allies to renew a high-pressure campaign against Iran.

U.S. officials have said that Iran sought to kill Mr. Trump in revenge for ordering the 2020 drone strike that killed Maj. Gen. Qassim Suleimani, the commander who directed Iran’s militias and proxy forces. The Department of Justice has issued two indictments that officials said were related to Iranian plotting against Mr. Trump.

American officials have also accused Iran of plotting to assassinate other Trump administration figures.

The officials interviewed for this story spoke on condition of anonymity to discuss sensitive diplomatic messages.

The message exchange was first reported by The Wall Street Journal.

The message from Iran repeated Tehran’s contention that the killing of General Suleimani was a criminal act, the two U.S. officials said. But it also said that Iran did not want to kill Mr. Trump, according to the U.S. officials, an Iranian official and an Iranian analyst who talks with both sides.

The Iranians said the message to the United States indicated that Iran sought to avenge the killing of General Suleimani through international legal means.

The U.S. officials said the Iranian message was not a letter from a specific official. But the Iranian official and analyst said it was from Iran’s supreme leader, Ayatollah Ali Khamenei.

Iran’s mission to the United Nations declined to comment on the message exchange. But it said in a statement that Iran was committed to responding to General Suleimani’s killing “through legal and judicial avenues.”

During the presidential campaign, American officials warned that Iran was plotting to kill Mr. Trump.

Federal prosecutors in Manhattan said last week that Iranian plotters had discussed a plan to assassinate him, which Iran’s Foreign Ministry called baseless.

In July, Asif Raza Merchant, a Pakistani man who had visited Iran, was arrested in New York and was later charged with trying to hire a hit man to assassinate American politicians. Investigators believe his potential targets included Mr. Trump.

Intelligence about Iran’s intentions was provided to the Secret Service, which added counter-sniper teams to Mr. Trump’s protective detail ahead of the assassination attempt on him in July, in Butler, Pa., by a lone gunman with no ties to Tehran, according to U.S. officials.

Iran had considered Mr. Trump to be a difficult target because of his Secret Service protection. But after the attempted assassination in Pennsylvania and another near Mr. Trump’s golf course in Florida, U.S. intelligence agencies assessed that Iran grew more confident that the former president could be successfully targeted.

That assessment of a growing threat, combined with the attempts on Mr. Trump’s life, prompted both an intense security review and a diplomatic campaign to convince Iran that it was making a grave miscalculation, according to officials.

Elon Musk, who has become a close ally of Mr. Trump, met with Iran’s ambassador to the United Nations on Monday, at Mr. Musk’s request, the Iranians said — a sign that it is not only the lame duck Democratic administration that is looking to avoid a direct clash, but also the Trump camp. The Iranians said the meeting with Ambassador Amir Saied Iravani, at a secret location in New York City, was about defusing tensions between Iran and the United States under the Trump administration.

Mr. Musk did not respond to a request for comment.

The United States and Iran have not had official diplomatic relations since Iran’s 1979 revolution, when 52 Americans were taken hostage in the U.S. embassy in Tehran, and held for more than a year.

The Swiss embassy in Tehran is the official diplomatic liaison between the two nations, but American and Iranian officials have held direct and indirect negotiations in recent years on a host of issues, including Iran’s nuclear program, regional tensions and swapping detainees.

The U.S. and Iranian messages were sent through the Swiss, according to the Iranian official and the analyst.

Observers of President-elect Donald Trump have long known the folly of trying to predict his decisions. But when it comes to foreign relations, especially in the Middle East, there are some ways that his second term will undoubtedly be different from his first.

The region has changed drastically since Hamas’s Oct. 7 attacks on Israel, which have disrupted the balance of power and the priorities of its major players.

It is impossible to say what’s coming. But my colleagues have conducted extensive reporting on everything that has changed, and this seems like a good moment to draw together some of their findings.

Oct. 7 attacks

Hamas’s attack on Israel on Oct. 7, 2023, was one of those moments that divides history into “before” and “after.” In the attack, Hamas massacred civilians in Israel and took others back to Gaza as hostages. As my colleague Steven Erlanger wrote just two weeks later, the assaults shattered longstanding assumptions about the Israeli-Palestinian conflict, ushering in a period of violent uncertainty.

In Trump’s first term and through much of President Biden’s, Palestinian demands for statehood received little attention. Israel controlled the West Bank and contained Gaza so tightly that it seemed that status quo might endure indefinitely.

But Hamas’s attack, and the wars and realignments that followed, have changed everything. The United States is once again deeply involved in the region, where it has provided military support for Israel’s war against Hamas in Gaza and against Hezbollah in Lebanon. And widespread anger over the conduct of Israel, which has killed tens of thousands of people and displaced over a million, has brought renewed attention to the issue of Palestinian statehood.

Israel and Iran’s disrupted equilibrium

Before Hamas’s Oct. 7 attacks last year, Israel and Iran were in a state of occasionally violent but largely stable equilibrium. They were engaged in a shadow war, but neither wanted all-out conflict, and they maintained a rough balance of mutual deterrence.

That equilibrium was shaken on Oct. 7. It was further undermined this year when Israel conducted an airstrike on an Iranian diplomatic facility in Syria, was suspected of assassinating a Hamas leader in Tehran and decimated the leadership of Hezbollah. Iran launched two separate large-scale missile attacks on Israel, its first ever, which Israel met with carefully calibrated strikes against Iran’s air defenses and missile production facilities.

As I’ve written in recent columns, if Israel and Iran fail to reach a new balance of deterrence against each other, their conflict could intensify, potentially drawing in other countries.

Saudi Arabia and Iran: From cold war to détente

For most of the 2010s, Saudi Arabia and Iran used proxy battles to fight a cold war in the Middle East. Their rivalry provided a kind of decoder ring for the region’s many civil wars as well as the sectarian tensions between Sunni and Shia Muslims: Iran backed Shiite militant groups throughout the region, while Saudi Arabia sought influence via Sunni proxies of its own.

That has begun to change. In March 2023, China brokered a deal re-establishing relations between Iran and Saudi Arabia. As my colleagues Farnaz Fassihi and Vivian Yee reported, the countries agreed to reopen embassies; revive an old security pact; not attack each other, even through proxies; tone down the rhetoric in the news media; and not meddle in each other’s domestic affairs.

Many of those promises are, at present, aspirational rather than real. “I would call it a cautious détente, a cautious opening up, a cautious willingness just to work together to de-escalate,” said Anna Jacobs, a senior Persian Gulf analyst for the International Crisis Group.

The thaw in relations was on prominent display this week, as my colleague Ismaeel Naar reported. On Sunday, the Saudi and Iranian military chiefs met in Tehran. That same day, the Saudi Press Agency reported, the president of Iran spoke directly to Mohammed bin Salman, the crown prince of Saudi Arabia and its de facto ruler, by phone.

That dialogue “sends a really powerful message, especially with Trump’s re-election, that the region is very different from Trump’s first term,” Jacobs said. “The relationship between Saudi Arabia and Iran is very different now.”

A setback for an Israel-Saudi pact

Before the Oct. 7 attacks, Saudi Arabia and Israel seemed on the cusp of an agreement to normalize their relations that had the potential to reshape the Middle East. Prime Minister Benjamin Netanyahu of Israel hoped that such a deal would lead to the creation of a kind of Middle Eastern NATO, creating closer security ties between Israel and the Gulf States while further isolating Iran and its allies.

Now, things look very different. Israel’s wars in Gaza and Lebanon have made it untenable for Saudi Arabia and other countries to make a deal with Israel unless they extract significant concessions, possibly including a commitment to Palestinian statehood — but Israeli opposition to a two-state solution is now stronger than it has been in decades.

Coupled with the détente between Iran and Saudi Arabia, that raises the possibility of a new regional order in which Israel, rather than Iran, becomes more isolated.

The unpredictability of Trump Part II

In Trump’s first term, many argued that he was following the “madman strategy” in foreign affairs. That’s the idea that if your opponents think you are unstable enough to follow through on a threat despite potentially disastrous consequences, they’re more likely to back down.

While there may be some strategic logic for following the madman strategy against adversaries, behaving erratically with friendly countries can cause them to pull away and seek other alliances.

In 2019, a missile attack hit Saudi Arabia’s major oil installations at Abqaiq and Khurais. The U.S. accused Iran of carrying out the strike, though the Houthi rebel group, an Iran-backed militia in Yemen, claimed responsibility. Trump said that there was “no rush” to respond because he didn’t want to involve the U.S. in a war.

That response appears to have contributed to the Saudi decision to pursue a reset with Iran, according to a report from the International Crisis Group.

The second Trump administration may bring more mixed signals. As my colleagues Lara Jakes and Adam Rasgon have written, Trump’s nominees for the top diplomatic envoys to the Middle East have little foreign policy background but have signaled fervent support for Israel.

And although Trump has long taken a harsh line on Iran, this week Elon Musk, a close adviser of the president-elect, met with two Iranian officials to discuss ways to defuse tensions between Iran and the United States, my colleague Farnaz Fassihi reported.

The Israeli military kept up its heavy bombing of a once densely populated area adjoining Beirut on Friday after saying its ground troops were battling new targets in southern Lebanon, signaling a widening of the fighting that could further undercut cease-fire efforts.

The airstrikes on the Dahiya area south of Beirut, where the militant group Hezbollah holds sway, were the latest in a string of bombings this week. The Israeli military issued new evacuation warnings just after dawn on Friday, and missiles began landing soon afterward, leveling at least one high-rise residential building that had been identified in the warnings and sending a thick dust cloud through the surrounding streets.

There were no immediate reports of casualties. Most residents fled the Dahiya weeks ago, when Israel’s bombing campaign began.

There were also signs that Israel’s ground invasion was broadening and that its troops were battling Hezbollah fighters deeper inside Lebanese territory.

The Israeli military said on Thursday that its commandos were conducting ground operations against “several new enemy targets” in Lebanon. A senior Lebanese security official, speaking on condition of anonymity to discuss sensitive military matters, said Israeli ground forces were operating around the town of Chamaa, roughly three miles from the border.

Hezbollah also said overnight that it had attacked Israeli soldiers near Tayr Harfa, a town south of Chamaa that it described as part of its “secondary line” of defense and where clashes had not been previously reported. On Friday, the group said it had fired rockets at Israeli troops on the outskirts of Talloussah, another town where fighting had not been previously reported.

A widening Israeli offensive would undermine U.S. diplomatic efforts to stem the conflict between Israel and Hezbollah, which is backed by Iran. The Biden administration has renewed a push to contain the fighting after rounds of shuttle diplomacy over the past year failed.

Israel has demanded that Hezbollah withdraw from areas near the Israel-Lebanon border as part of any truce. Israel has also insisted that any cease-fire deal preserve its right to attack Hezbollah again should the group violate the terms of a truce, a stance that the Lebanese government and Hezbollah strongly oppose.

There has been no public indication that Hezbollah or its patron, Iran, are willing to acquiesce to Israel’s demands. While Hezbollah’s leaders and weapon stockpiles have been hit hard, the group still poses a formidable threat, firing rockets and drones into Israel daily and killing six Israeli soldiers on Wednesday in southern Lebanon.

A prominent Iranian official, Ali Larijani, met on Friday with Lebanese officials in Beirut to discuss the cease-fire efforts, the Iranian Embassy in Lebanon said. Hezbollah is Iran’s most powerful regional proxy, and any diplomatic settlement would almost certainly be contingent on Tehran’s approval. A day earlier, Mr. Larijani was in Syria, where he met with President Bashar al-Assad.

Two Iranians affiliated with the Islamic Revolutionary Guards Corps said Mr. Larijani, a senior adviser to Iran’s supreme leader, Ayatollah Ali Khamenei, had passed along messages to Hezbollah from Mr. Khamenei that said he supported ending the war with Israel, and that Iran would continue its support and help the group rebuild its forces and recover from the war.

The Iranians, who were granted anonymity because they were not authorized to speak publicly, said the Iranian leader had also told Hezbollah to accept the terms of a cease-fire deal demanding it move its forces north, in accordance with U.N. Security Council Resolution 1701, which ended a previous round of fighting between Israel and the armed group.

Asked to comment on reports that U.S. officials had given the Lebanese government a draft cease-fire proposal, Mr. Larijani said his visit had not been intended to “undermine” U.S.-led diplomatic efforts, Lebanon’s state-run news agency reported.

“We want to solve the problem,” Mr. Larijani said.

This month, Hezbollah’s leader, Naim Qassem, called the U.S.-led efforts to stem the conflict with Israel futile, saying that the only way to end the war was “on the battlefield.” Still, he did not reject the potential for negotiations on suitable terms.

“We are ready for a long war,” he warned.

Israel began an intensified military campaign against Hezbollah in September, nearly a year after the group began firing rockets into Israel in solidarity with Hamas in Gaza. The Israeli offensive set off a humanitarian crisis in Lebanon, displacing nearly a quarter of the population and buckling the country’s health system.

Although Israel’s military leaders had hoped to conduct a limited ground operation that focused solely on the first line of Lebanese villages along Israel’s northern border, they decided to slightly expand that range, Amir Avivi, a retired Israeli brigadier general, said in an interview.

The reason, he said, was that Israeli military officials realized they needed to do more to clear out Hezbollah’s military installations and believed that a broader offensive could force the group into making a diplomatic settlement on terms favorable to Israel.

“There’s an understanding that we need to ramp up the pressure and clear out a greater area, and that’s what they’re doing” Mr. Avivi said.

Early in the war, the Christian villagers of Aitou in Lebanon’s far north rarely heard the buzz of drones or the sounds of bombs exploding — daily occurrences in the south, where Israel is battling the Shiite militant group Hezbollah.

Then a displaced Shiite family of tobacco farmers from the south arrived in Aitou, seeking refuge.

In the days that followed, more relatives joined the family. On Oct. 14, a man who was believed to be distributing aid money for Hezbollah drove up to the house where the family was staying and took bags full of cash inside, according to two neighbors and a man who delivered water to the family.

Minutes later, an Israeli airstrike flattened the house and killed the entire family along with the man who had brought the money. Some of the bills, both U.S. dollars and Lebanese pounds, were seen blowing in the air at the site immediately after the blast.

Only a statue of St. Charbel, a Maronite saint, remained standing just below the destroyed building.

The Israel-Hezbollah conflict escalated drastically in September, sending hundreds of thousands of people, mostly Shiite Muslims from southern Lebanon, fleeing their homes. Many sought refuge in areas dominated by other faiths and sects and Israel’s bombardments seemed to track the displaced as they dispersed across the country. Strikes like the one on Aitou, outside of Hezbollah-dominated southern Lebanon, began to rise.

These attacks disrupted life in previously safe places, inflaming sectarian tensions that have long smoldered just below the surface of Lebanese society. They spread a fear that wherever the displaced turned up, Israeli bombs would follow.

Asked about the attack on Aitou, the Israeli military said only that a strike on northern Lebanon in mid-October had targeted a Hezbollah figure and it was checking whether Lebanese civilians had been killed. Lebanese military officials said that they did not know the identity of the man who had brought the money.

But neighbors who came to commiserate with the Christian owners of the bombed house vented frustration with Hezbollah, the most powerful military and political faction in Lebanon, which seeks Israel’s destruction.

Elias, a Christian friend of the landlord, urged Hezbollah to defeat Israel if it could.

“But if not, shut up. Don’t invite them here,” said Elias, 54, who asked to be identified by his first name only for fear of repercussions. “You gave them a big invitation with your shelling,” he added, referring to Hezbollah’s attacks on Israel over the past year in solidarity with Hamas in Gaza after Hamas led the Oct. 7, 2023, attack on Israel that set off the war.

A small country of just over five million people, Lebanon has long been divided along sectarian lines. Maronite and Orthodox Christians, Druse, and Sunni and Shiite Muslims, who follow somewhat different interpretations of Islam, are just some of the communities that hold sway.

Sectarian divisions fueled the country’s 1975-90 civil war, which ended with a renewed division of power along religious and sectarian lines. The result has been political paralysis and a dysfunctional state that lacks even a working power grid.

Many of the warlords responsible for the civil war are still prominent political players 30 years later.

The horrors of the civil war still haunt Lebanese society — so much so that the defense minister in late October held a news conference in which he specifically warned against “fitna,” Arabic for “civil strife,” and made clear that he saw a grave danger in anything that stoked religious or sectarian divisions.

When the displaced first began to arrive in other communities, they found widespread sympathy from fellow citizens who gathered blankets and food and helped them find shelter in an extraordinary show of solidarity. But then came the Israeli airstrikes, and warmth gave way to worry that Hezbollah members might be among the fleeing crowds.

Tens of thousands of Shiite families in Lebanon receive financial support from Iran-backed Hezbollah, and the group has been handing out modest sums to some of those forced from their homes.

As the months passed, the numbers of displaced swelled, surpassing a million.

“They are in schools, in empty buildings, in villages. Wherever they go, people are afraid,” said Rabih Haber, a Lebanese political consultant. “Why? Because a small number will be armed, a small number will be targets.”

The Israeli airstrike on Aitou was so powerful that it killed the entire displaced Shiite family, 21 people, the Lebanese Health Ministry said. Some were children, according to the local hospital and the Christian landlords who had rented to them.

The blast reduced the house to rubble and sowed fear in the community that the same could happen if other displaced Shiite families sought refuge there.

“Something like this never happened in Aitou,” said Sarkis Alwan, 54, the brother of the landlord. “We never thought it would reach here.”

Elias, the landlord’s friend, had stopped by to commiserate after the airstrike. He said that his own family had long lived in the Aitou area.

“This is what will remain of our country — a pile of rubble and twisted wires,” he said.

The shift from welcome to wariness to hostility toward the uprooted population came quickly, said Yara Abdel-Naby, 21, a Shiite university student from the village of Bnaafoul in southern Lebanon.

She said her family lived so close to their Christian neighbors that when Israeli bombs started falling around Bnaafoul, the first place in which they took refuge was a church. They then moved to the house of a Christian friend, who let them stay for free.

“We thought for sure they would not bomb the church,” she said.

But after two weeks, the bombs grew so close and so frequent that her family felt compelled to move on. They encountered increasing distrust toward Shiites as they ventured north, Ms. Abdel-Naby said.

The most painful experience, she said, came when, after wandering from one makeshift accommodation to another, they found a place to rent in Chouf, a predominantly Christian and Druse region in central Lebanon.

When they arrived, the woman who owned the house saw Ms. Abdel-Naby with her long hair uncovered and was welcoming, Ms. Abdel-Naby recalled. But when Ms. Abdel-Naby’s mother and another relative emerged from the car in the head scarves and long robes that many Shiite women wear, the homeowner’s demeanor changed.

Soon she was finding excuses why the family could not stay, Ms. Abdel-Naby said. There were too many people, there would not be enough water. Their host complained that the new arrivals were making the place dirty.

Her family had paid for four days. But during their first night, their host informed them that someone else would be coming in the morning. They had to leave.

“Because of the situation, it is easier now for people to say these things,” Ms. Abdel-Naby said. “Before, they were embarrassed to show it. But now, it just gets worse every day.”

In other towns dominated by Christians and Druse in the mountains east of the capital, Beirut, people started to find leaflets in late October warning anyone associated with Hezbollah or Amal, another Lebanese Shiite faction, to leave the area “for your safety and our safety.”

In Beirut, an Armenian Christian mukhtar, or community leader, said that he, like a number of other mukhtars, had set up a hotline for residents to report to when they suspected that newly arrived displaced people who were renting in the neighborhood might be connected to Hezbollah.

The predominantly Christian neighborhood of Achrafieh in Beirut is now marked with the white flags of the Lebanese Forces, a Christian party. The flags function almost as a fence, signaling to displaced Shiites looking for a place to stay that they are unwelcome here.

“We don’t want anyone with a party background here,” said Maroun, 60, a dental technician, referring to Hezbollah, whose name means Party of God. He also asked to be identified by only his first name for safety reasons.

“Of course we feel solidarity with people who are displaced,” he added. “But we don’t want to endanger our families. We don’t want this war. It’s not our war.”

Patrick Kingsley contributed reporting from Jerusalem.

German Chancellor Olaf Scholz and President Vladimir V. Putin of Russia spoke by phone for an hour on Friday, the first discussion between Mr. Putin and a sitting leader of a large Western country since late 2022.

German authorities said the call centered on prospects for ending the war in Ukraine.

The Kremlin confirmed the conversation and said Mr. Scholz initiated the call.

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The various institutions of postwar Europe were intended to keep the peace, bring warring peoples together and build a sense of continental attachment and even loyalty. From the growth of the European Union itself to other, softer organizations, dealing with culture or sports, the hope has always been to keep national passions within safe, larger limits.

But growing antisemitism, increased migration and more extremist, anti-immigrant parties have led to backlash and divisions rather than comity. The long war in Gaza has only exacerbated these conflicts and their intensity, especially among young Muslims and others who feel outraged by Israeli bombings and by the tens of thousands of deaths in Gaza, a large proportion of them women and children.

Those tensions were on full display in the recent violence surrounding a soccer match between an Israeli and a Dutch team in Amsterdam, where the authorities are investigating what they call antisemitic attacks on Israeli fans, as well as incendiary actions by both sides. Amsterdam is far from the only example of the divisions in Europe over the Gaza war and of the challenges they present to European governments.

The normally amusing Eurovision Song Contest, which was held this year in Malmo, Sweden, a city with a significant Muslim population, was marred by pro-Palestinian protests against Eden Golan, a contestant from Israel, which participates as a full member.

The original lyrics to her song, “October Rain,” in commemoration of the 1,200 Israelis who died from the Hamas-led attack on Oct. 7, 2023, which prompted Israel’s response in Gaza, were rejected by organizers for their political nature, so were altered to be less specific. Her performance was met with booing and jeering from some in the audience, but she did receive a wave of votes from online spectators, pushing her to fifth place.

It was hardly the demonstration of togetherness in art and silliness that organizers have always intended.

In Germany, where supporting the existence of Israel is a “Staatsräson,” a fundamental principle of the German state, there have been numerous examples of anti-Israel and pro-Palestinian rallies. Palestinian supporters say they, too, have felt marginalized, their voices unheard or unheeded.

The police in Germany have shut down pro-Palestinian conferences and denied entry to pro-Palestinian speakers, while some German art organizations have withheld prizes to authors whom they have deemed to have been overly critical of Israel or of Israeli conduct in Gaza or the West Bank.

A year ago, the Frankfurt Book Fair was accused of “shutting down” Palestinian voices, after an awards ceremony to honor “Minor Detail,” a novel by a Palestinian author, Adania Shibli, was canceled because of the war between Israel and Hamas.

Just this week a documentary film about life in the occupied West Bank that won the Berlin film festival this year, “No Other Land,” opened in German cinemas with renewed charges that it exhibits “antisemitic tendencies,” according to the Berlin city website Berlin.de.

The director of the festival, Tricia Tuttle, rejected the charge, and the website changed its wording.

“The Gaza war has infected everything,” said Stefan Kornelius, a senior editor of the German daily Süddeutsche Zeitung. “The war causes people to position themselves and support a one-sentence verdict on the Mideast,” he said. “It often runs counter to German Staatsräson on Israel, which supports Israel whatever it takes, and that counterreaction, especially in the arts, causes people to back the Palestinians with some intensity.”

What took place in Amsterdam, however, was of a different order and shook many in Europe beyond the Netherlands.

The match last week between an Israeli team, Maccabi Tel Aviv, and Amsterdam’s Ajax, was part of the Europa League competition run by the Union of European Football Associations, best known as UEFA.

While soccer has always been a deeply partisan sport, stoking nationalism and sometimes related violence, the sport’s near universality also provides a common bond and players from one country often play on teams in others.

Fearing the kind of violence seen in Amsterdam, the authorities in France, which like the Netherlands has a significant minority of Arab and Muslim citizens, deployed an extra 4,000 police officers for a soccer match Thursday evening on the outskirts of Paris between the national teams of Israel and France.

President Emmanuel Macron, his prime minister and two former French presidents attended the match in a show of solidarity against antisemitism, and though demonstrators protested nearby, there was only a minor skirmish in the stands that the police quickly controlled.

Passions have been running high. In Germany, Berlin police are investigating reports that a youth team of Makkabi Berlin, a Jewish football club, was chased by a crowd yelling “Free Palestine” and bearing sticks and knives after a match with another Berlin club. The police said that they were investigating the incident on grounds of breach of the peace, incitement and insult.

If Oct. 7 changed so much for Israel and Jews abroad, Israel’s asymmetric response, which has brought accusations of multiple war crimes and even genocide, has changed much for Arabs and Muslims in Europe, too. Many Muslims in Europe say they feel threatened themselves.

The rise of extremist nationalist parties like the Alternative for Germany, which has numerous neo-Nazi members and has used racist language to condemn immigration and call for the expulsion of nonnative German citizens, has heightened those anxieties.

Aiman Mazyek, chairman of the Central Council of Muslims in Germany, said that there is “a climate of fear” among Muslims since Oct. 7.

“Many Muslims in our country are uneasy, they’re afraid to speak out at all, and feel intimidated by the debate,” he said. There have been attacks on mosques and “on Muslims and also those who are perceived to be Muslims at a rate like never before,” he said.

According to the European Union Agency for Fundamental Rights, which monitors both antisemitism and anti-Muslim discrimination, nearly one in every two Muslims in the bloc face racism and discrimination in their daily lives, a sharp increase since 2016, it said in a report last month.

They are targeted, the report said, not just because of their religion, but also because of their skin color and ethnic or immigrant background. Young Muslims born in Europe and women wearing religious clothing are especially affected, the report said, and many face racial profiling by the police.

Given the heightened atmosphere, there was much attention on Thursday’s France-Israel match.

Hélène Conway-Mouret, vice president of the foreign affairs and defense committee of the French Senate, said that feelings among young Muslims were running especially high because of the horrors of the long Gaza conflict and confusion about where they belong.

“There is a real identity issue with second and third generation Muslim immigrants,” she said. “Their parents knew they were Moroccan, for example. But their children wonder, ‘Are they Moroccan,’ and yet they are not.” Nor are they always accepted as French, and face significant discrimination.

In a way, she said, support for the Palestinians “brings them together as a community.”

There have been nearly 70 arrests so far in Amsterdam, including 10 Israelis, for mostly minor offenses. Dutch officials have decried the attacks in Amsterdam as antisemitism, including what they said was an orchestrated effort to seek out Jews, as they also investigate inflammatory actions and vandalism by some Israeli fans.

“What happened over the past few days is a toxic cocktail of antisemitism, hooligan behavior and anger over the war in Palestine and Israel, and other countries in the Middle East,” Femke Halsema, the mayor of Amsterdam, wrote to the City Council.

“Antisemitism can’t be answered with other racism,” she added. “The safety of one group cannot be at the expense of the safety of another.”

It began with a polite plea on social media from the leader of Canada.

“It’s me, hi,” Prime Minister Justin Trudeau wrote to Taylor Swift on X, using a reference to her lyrics. “I know places in Canada would love to have you. So, don’t make it another cruel summer. We hope to see you soon.”

Canada was not on Ms. Swift’s list of concert destinations last summer when she announced a batch of new shows for her tour. Or maybe she was just saving the best news — at least for Canadian fans — for last.

Now, Ms. Swift is wrapping up her blockbuster Eras Tour in Canada, sending Toronto into a glittery frenzy. Her shows have become cultural events in every city she plays, jolting local economies, uniting legions of fans and mobilizing cities around her star power.

“The Eras Tour is kind of the Woodstock of our generation,” said Jasmeet Sidhu, a Canadian photographer and director who was showcasing her images of Ms. Swift’s past performances.

Ms. Swift’s version of Woodstock, while more commercial than activist, has certainly delivered on unity: Witness the multicolored friendship bracelets that her fans — who call themselves Swifties — have taken to making, wearing and trading.

Ms. Swift is scheduled to perform six shows in Toronto, which are expected to draw 240,000 concertgoers, before heading to Vancouver for three shows, ending the tour on Dec. 8.

Many people are desperate to catch a final glimpse.

They include Stephanie Jenkins of Charlotte, N.C., and her 12-year-old daughter, Ellen, who had been en route to Vienna when news broke that Ms. Swift’s show there had been canceled following a foiled terrorism attack.

Earlier shows in the United States were sold out, Ms. Jenkins said. She hadn’t been able to get tickets for the Toronto concerts, but she and her daughter decided to go anyway, driving 12 hours from home.

On Thursday, they were outside the Rogers Center, the concert venue, with Ms. Jenkins holding a sign describing their quest to see Ms. Swift and frantically hitting refresh on her cellphone, trying to find tickets that were close to her $600-a-ticket budget.

“She’s the only person I know who would do this for me,” said Ellen, 12.

Mission accomplished: mother and daughter triumphantly entered the stadium before Ms. Swift took the stage.

Outside, a daunting line of ticket holders had formed hours before the show. Fans wore enough glitter and sparkles to compensate for overcast and eventually rainy skies.

Evidence of hours of careful costume planning abounded: shimmery tinsel woven into hair, opalescent eye shadow, shiny gemstone stickers configured into face tattoos.

Even the Toronto Police, while mobilizing a major show of force, contributed some Swiftie love. Police horses wore giant friendship bracelets around their necks, while officers collected and traded the human-sized versions.

And Myron Demkiw, the chief of police, photobombed into some of the selfies being taken in front of a tour sign.

“Everybody’s in a great mood,” said Sgt. Stephen Hammond, a police spokesman.

Of course, on social media, the mood also swung the other way, with complaints that a main highway had been cleared for a police motorcade to escort Ms. Swift to the stadium.

There was more irritation when the city temporarily mounted 22 ceremonial street signs in Ms. Swift’s honor, having to clarify that it did not use any tax dollars. The Rogers Center footed the bill.

As Ms. Swift’s shows have done in other places, the event will boost the economy, with more than 152 million in Canadian dollars (about $108 million) in direct spending, mostly by visitors from outside Toronto, according to Destination Toronto, a tourism organization.

Brian Dagg of Winnipeg wore a T-shirt proclaiming his financial contribution to Swiftmania: “Spending a Lot of Money at the Moment,” it said. He had flown in with his wife and daughter, spending about 3,500 in Canadian dollars (roughly $2,500) on flights and tickets alone.

Silver lining: They were saving money on high hotel prices by staying with family, and it was a worthy Christmas gift for his daughter, Maddyn, 12, who would be attending her first concert.

People of all ages were in the audience, but for the generation of women around Ms. Swift’s age, 34, her music heralded them into womanhood.

For Stacy Wetmore, 31, Ms. Swift’s earlier hits, like “Teardrops On My Guitar,” would be on repeat in the mornings when she got ready for school. She and her friends Kyra Clark and Taylor Fischer had traveled from Columbia, Md., with tickets for Saturday’s show.

“Listening to these songs, you’re like, wow, I’ve been through something like that,” Ms. Fischer said. “It feels good to be seen.”

As Jenny Palmiotto and her daughter, Grace, prepared to enter the stadium on Thursday, they reflected on how the tour had prompted them to visit new places to see her perform, far from their home in San Diego.

“We’ve never been to Poland or Sweden, and now, Canada,” said Ms. Palmiotto. There is an energy that keeps drawing them back, she explained. “It’s the best part of humanity here at this show.”

The tiny copper gladiator stands ready for battle, decked out in a helmet and armor, an elaborate shield held in front as if bracing for his opponent’s blows.

The figure, just three inches tall, is some 2,000 years old, and was once perched on the handle of a knife. It was found almost three decades ago by a diver in the river Tyne, near Hadrian’s Wall in the north of England, which was for hundreds of years the northern frontier of the Roman Empire.

The knife handle remained in the diver’s private collection until it was recently offered on loan to English Heritage, a charity that manages many of the country’s historic monuments.

It will go on display in the museum at Corbridge Roman Town at Hadrian’s Wall next year, the charity said on Friday in a well-timed announcement that coincided with the release in Britain of Ridley Scott’s “Gladiator II” film, starring Paul Mescal.

Experts say the copper figure is evidence of how the celebrity status of gladiators reached into every corner of the once sprawling Roman Empire, including the far-flung outposts of Britain.

“It is rare to find a piece of gladiator memorabilia in Britain and to find such a well-preserved and interesting piece is particularly remarkable,” said Dr. Frances McIntosh, English Heritage’s curator for Hadrian’s Wall and the North East, in a statement.

Gladiators were enslaved, but despite that status, they could become major celebrities, as the bloody spectacles of the gladiator games played a major part in Roman cultural life, Dr. McIntosh said. As a result, gladiators inspired memorabilia from ceramics to cups to figurines.

According to English Heritage, the figure is a secutor, a class of gladiator with specific armor. The charity noted that the knife handle depicts a “strong muscular fighter with heavy equipment including a large shield sword and helmet,” and said that because it appears to be left-handed, which would have been considered unlucky at the time, the figurine could even represent a specific person.

The figure was found at Corbridge Roman Town, a historic site now managed by English Heritage and nestled along Hadrian’s Wall in Northumberland, once a key defensive fortification at the Roman Empire’s northwestern reaches.

The man who discovered it will lend it to English Heritage, along with other Roman objects he found in the river, for an exhibition next summer.

Corbridge, now an archaeological site where visitors can walk through the remains of town streets, was for hundreds of years a bustling supply stop for Roman civilians in the area. It remained so until the end of the Roman presence in Britain at the start of the fifth century, when it was abandoned.

Britain was part of the Roman Empire for almost 400 years, beginning in 43 A.D. with an invasion under the emperor Claudius and lasting until around 410 A.D. when Roman troops withdrew from the island back into continental Europe. But the Roman era forever shaped the island, leaving behind a vast network of roads, fortresses, grand baths and villages.

And, it appears, they left behind some of their fan memorabilia too.