Iran vowed revenge at the end of last month after a top Hamas leader was killed in Tehran, leading many in Israel to fear an imminent attack. Nearly two weeks have passed and no large-scale response has materialized, leaving Israel and the wider Middle East on edge.

The crisis comes at an especially delicate moment in Iran, which analysts say is trying to formulate a response that doesn’t let an assassination on its soil go unpunished, while avoiding an all-out war against a powerful adversary. It also comes as a new government in Tehran has taken office, which could be slowing a decision on how to respond.

Here’s a look at the crisis and the factors that could determine what happens next:

Why has Iran vowed revenge?

Iran and Hamas officials have promised to avenge the death of Ismail Haniyeh, a senior Hamas leader, who was killed in Tehran on July 31 after he attended the inauguration of Iran’s president, Masoud Pezeshkian. Iran, which backs Hamas, blamed Israel for the assassination. Israeli leaders have not said their forces were responsible.

A day earlier, Fuad Shukr, a senior commander in Hezbollah, which is also supported by Iran, was killed in an Israeli airstrike in a suburb of the Lebanese capital, Beirut. The Israeli government said that strike was in retaliation for a rocket fired from Lebanon that struck a soccer field in the Israeli-controlled Golan Heights, killing at least 12 people, mostly teenagers and children. Hezbollah has denied carrying out that attack.

But Mr. Haniyeh’s killing was seen as the greater blow to Tehran because it took place on Iranian soil. In response, Iran’s supreme leader, Ayatollah Ali Khamenei, issued an order for Iran to strike Israel directly, according to three Iranian officials briefed on the matter.

Why hasn’t Iran responded yet?

A spokesman for Iran’s Foreign Ministry, Nasser Kanaan, said that “it is necessary to punish Israel,” echoing comments from other senior Iranian officials. But he also said that “Tehran is not interested in escalating the regional conflicts.”

Furthermore, the new president’s cabinet, including the foreign minister, is yet to be approved, which is likely to have slowed internal deliberations, said Sanam Vakil, a Middle East analyst at Chatham House, a research group in London.

At the same time, Mr. Pezeshkian, who is seen as a reformist, may try to balance a perceived need to project strength with his government’s broader interest in alleviating the effects of Western economic sanctions and in preventing Iran from becoming further isolated internationally, Ms. Vakil said.

“The response has to be carefully calibrated so as not to slam shut the door of negotiations with the West that could lead to potential sanctions relief,” Ms. Vakil said.

A military response that is viewed as largely symbolic is also risky from Tehran’s perspective, but it would be unlikely to deter Israel from conducting further attacks, said Ali Vaez, the Iran project director of Crisis Group, a think tank.

That leaves the option of a substantive response, but that would, in turn, likely provoke a bigger Israeli response — and Tehran would not be able to control the cycle of escalation that could follow, Mr. Vaez said.

“Israel has checkmated Iran in this situation because Iran is left with no good options,” said Mr. Vaez. He and Ms. Vakil both said that it is difficult to discern Iran’s intentions.

What could an Iranian response look like?

Iran could strike Israel from multiple directions and in different forms. Tehran maintains a network of proxy forces including Hamas, Hezbollah and the Houthi militia in Yemen, giving it the ability to attack targets from northern Israel to the Red Sea.

In April, Tehran attacked Israel with around 300 missiles and drones, a response to an apparent Israeli strike on an Iranian embassy complex. Almost all were shot down by Israel’s air defenses assisted by the United States and other allies. It was the first direct attack by Iran after a clandestine war with Israel that had been conducted for years by land, sea, air and cyberspace and, as such, represented a significant escalation.

The attack in April caused light damage to an Israeli air base in the Negev desert and seriously wounded a 7-year-old girl. Now Israel is bracing for what could be a bigger attack.

How is Israel preparing?

The Israeli authorities have told people to stock food and water in fortified safe rooms, and hospitals have made plans to move patients to underground wards. At the same time, rescue teams have been positioned in cities.

U.S. and Israeli diplomats and security officials had some advanced knowledge of its scope and intensity of Iran’s attack in April, which facilitated defensive preparations. By the same token, the nearly two weeks that have passed since Mr. Haniyeh’s killing have allowed time for heightened readiness in Israel.

Last week, Prime Minister Benjamin Netanyahu said that Israel was “prepared for defense, as well as offense.”

That said, military analysts say that Iran and Hezbollah could potentially overwhelm Israel’s defenses by firing enough missiles simultaneously. They could also launch swarms of drones that fly at low altitude, making them difficult to detect and destroy.

How are the United States and others responding?

Diplomats have feared for months that back-and-forth strikes between Israel and Iran could escalate into a regional conflict that would compound both the war in Gaza and the conflict on Israel’s border with Lebanon. As a result, they have worked to forestall or minimize Iran’s reaction.

The foreign minister of Jordan, an ally of the United States, has traveled to Tehran in recent days for meetings. Saudi Arabia last week convened an emergency meeting of the Organization of Islamic Cooperation, a forum of Muslim countries, at which it called the assassination of Mr. Haniyeh a violation of Iran’s sovereignty while urging de-escalation by all sides.

The United States has stepped up its military readiness. Defense Secretary Lloyd J. Austin III has ordered additional combat aircraft, warships and a guided-missile submarine to the Middle East in response to threats, both to bolster Israel’s capacity to thwart any potential attack and to reinforce the message that it would support the country militarily.

At the same time, the Biden administration has sought to jump-start cease-fire talks for Gaza. The Biden administration and Arab mediators are planning a meeting in the region on Thursday to try to advance a deal. Israel has said it will send its negotiators, but Hamas has not said if it will participate.

Behind thickets of beech trees, overgrown with nettles and beside a blue lake an hour north of Berlin, a villa that once belonged to a Nazi mastermind quietly rots.

No one knows what to do with the estate beside the Bogensee lake in Brandenburg. It was built for Joseph Goebbels, the Nazi propaganda minister, by his grateful country just before the start of World War II. Owned by the State of Berlin today, it has sat moldering expensively on the public’s tab, along with a set of dramatic dormitories built later by the Communist Party to house an indoctrination school. It is a nearly 20-acre campus that echoes with the pasts of two totalitarian regimes.

Too burdensome for the state to continue carrying, prohibitively expensive for most real estate prospectors and tainted by history, Berlin has given up on selling or developing it.

Instead, it has offered to give the Nazi mansion away, free. (The taker, of course, would be subject to the government’s approval.)

In exasperated comments made to Parliament this spring, Stefan Evers, the state’s senator for finance, made the pitch — take it off our hands, or we will tear it down — setting off a flurry of interest in prospective takers from around the globe.

There were inquiries from a dermatologist who wanted to open a skin-care center and from a few bargain hunters, Mr. Evers said recently in an interview in his offices in Berlin. None have been suitable, he said.

An earlier inquiry, from an extreme-right group called the Reichsbürger movement, seemed to embody the authorities’ worst fears. The group denies the legitimacy of the current German state; some of its members are on trial for a plot to overthrow the government.

Such attention — that the estate’s association with the Nazi era might attract an unsavory buyer — partly accounts for the villa’s neglect.

“The history of the place is precisely the reason why Berlin would never hand this building over to private hands where there would be a risk that it could be misused,” Mr. Evers said.

The fate of the villa is not only a logistical quandary for Germany. It illustrates a long-term and larger conundrum, the grounds of which have shifted over time, experts say: whether to preserve or obliterate the many edifices from Germany’s hateful past.

Directly after World War II, the prevailing approach was to move on, ignoring prior ownership, so as not to risk reifying it, according to Peter Longerich, a historian and the author of “Goebbels,” a biography. Hitler’s apartment in Munich, for example, has little information detailing its history; it has long been a police station in which officers still use Hitler’s own wooden bookshelves, he said.

The benefit of its law enforcement tenants is that their presence keeps at bay Nazi sympathizers who sometimes make pilgrimages to such sites. Last year in Austria, the government moved to convert Hitler’s birthplace into a police station for this reason, drawing contentious debate.

But as the far right has re-emerged in German politics, there has been a shift in sentiment toward remembering the past, in order to never forget it.

“The dominant attitude in education for a long time was to, if possible, ignore many things of this period,” Mr. Longerich said. “But nobody has a greater sense of coming to terms with the past than Germans have, so there is an ongoing process,” he added. “And it might be that over time, ignorance will need to be overcome and people find it necessary to preserve this space.”

Just outside the center of Wandlitz, the wildwood has grown up around the house, blocking the door to the private cinema where Goebbels screened his propaganda films. Cobwebs cloak bedroom windows. And motes of dust drift through airy salons where he wined and dined Nazi leadership, and where his six children played beside the hearth — until he and his wife poisoned them all in the war’s final days.

Maintenance of the property costs 280,000 euros a year (nearly $306,000) just to keep it from falling into shambles, according to the buildings department. Restoration would not only be expensive but introduce another thorny issue that dogs preservationists who must deal with former structures from both the Nazi and Communist chapters of Germany’s past.

“If they look too beautiful, you re-aestheticize their reign,” said Thomas Weber, a professor of history and international affairs at the University of Aberdeen, in Scotland. “But if you leave them but somehow destroy how they functioned at the time, then people will not understand, either.”

The mansion is filled with architectural flourishes that were popular among Nazi leaders, like its clever day-room windows that fold away into the floor — a touch also used in Hitler’s own vacation retreat in the Bavarian Alps. There is a bunker out back, too, just in case.

Other structures were added over time. Down a path, past headless concrete statues of intertwined lovers, are several almost Federal-style buildings. They were used as a Communist international youth college from the 1940s until the fall of the Berlin Wall. Up weed-sprouted steps and behind graffitied doors, their cavernous interiors hold barracks and an echoing auditorium.

It is a part of the site’s past often eclipsed by its Nazi heritage, said Gerwin Strobl, a modern history instructor at Cardiff University in Wales, who studies Germany. But it is one also painful to Germans. “In fact, it covers two German dictatorships in succession. That also explains why it is also so difficult to find a use for it,” Mr. Strobl said. “But buildings by themselves aren’t evil.”

On a bike ride on a recent Friday, a man and a woman in their 60s paused in front of what was the campus’s social center to take in the crumbling building. The pair, Marita and Frank Bernhardt, had met there as students in 1978.

She learned of its Nazi past only after reunification, Ms. Bernhardt said. “That’s why it has a bitter aftertaste,” she said of returning for the first time. And yet, it was where she and her husband had fallen in love. “The memories are still nice.”

After hearing about Berlin’s offer to give away the property, Rabbi Menachem Margolin, the chairman of the European Jewish Association, sent an open letter offering to convert it into an education center to counter all forms of hate.

“It is an important message to anyone,” Rabbi Margolin said. “That even the darkest place in the world can become a source of light.”

Such a project is worthy, Mr. Evers said, but the issue is financing. Walter Reich, the former director of the United States Holocaust Memorial Museum, said it was Germany’s obligation to help pay. “That’s part of the burden of German history,” Dr. Reich said in an email. “Germany’s unmasterable past.”

As the ash and alder creep over the villa, Oliver Borchert, the mayor of Wandlitz, has for years fended off interest from extreme right-wingers, including the coup-plotting Reichsbürger group.

The place needs more than upkeep — it needs transformation, Mr. Borchert said: “You have to find a use that can stand against and reflect the shadows of the house and its history.”

Audio produced by Jack D’Isidoro.

With cars being torched and mosques and hotels housing asylum seekers under attack, the riots that swept Britain over the past two weeks have posed the first direct challenge to the new prime minister, Keir Starmer.

But even if the violence has subsided, for now, at least, the shocking scenes of disorder have underscored the scale of the task facing his government.

That, analysts say, includes defusing tensions stoked successfully by far-right groups — over immigration and fraying public services — particularly in areas of Britain that have long been in economic decline.

While opinion polls show the public clearly supports Mr. Starmer’s crackdown on violent protesters, “a lot of those people who see the rioters as thugs want immigration brought down,” said Steven Fielding, an emeritus professor of political history at the University of Nottingham.

Mr. Starmer, who has promised to cut migration numbers, “needs to follow up and do the things he says he’s going to do,” Professor Fielding added, while noting that it was “no accident” that violence erupted in several economically deprived regions.

Concern over immigration, which declined in Britain after Brexit, is on the rise again and, when jobs are scarce and health care and other services are overstretched, immigrants make an easy target for the far right. The campaign leading up to last month’s general election prompted a bitter political dispute over the last government’s plans to send to Rwanda people arriving in Britain on small boats.

But while around 30,000 people entered the country that way last year, that was only a fraction of those admitted legally minus those who left — a number that hit almost 750,000 in 2022.

Sunder Katwala, the director of British Future, a research institute, said Mr. Starmer must show he can revive neglected areas where the rightists have found support by bolstering employment and public services.

“He needs to deliver,” Mr. Katwala said, “for those town and cities — whether it’s Southport or Hartlepool — where people’s primary concerns are National Health Service waiting lists and ‘Can I get a job?’”

Those close to Mr. Starmer say he is getting a grip on the disorder, drawing on his experience as a chief prosecutor in 2011, when riots took place in London and he pushed to get those responsible tried, sentenced and jailed swiftly to deter others.

“He has a detailed knowledge of how to do this, and he understands how you prosecute and convict quickly, and you do so visibly in a way that sends a message to anybody who is thinking about participating in one of these riots,” said Claire Ainsley, a former policy director for Mr. Starmer.

But ensuring that such violence does not recur is harder, she said.

“We have had the far right with us in good economic times and in bad economic times,” said Ms. Ainsley, who now works in Britain for the Progressive Policy Institute, a Washington-based research institute.

“But it is much harder for them to have any kind of influence when you are in better economic times,” she added. “That means people’s living standards rising and people starting to feel they are better off and that they are part of a system that is working — and that isn’t a description of Britain today.”

Ms. Ainsley pointed to the role of social media in spreading misinformation and stoking tensions, and cautioned against making a direct link between the riots and immigration. She noted that, alongside extremists, some of the rioters may be looters and other opportunists.

It is, she added, “wrong to assume that all of the people participating in these riots are politically motivated by immigration.”

Still, other analysts note the context of the riots, after years of broken promises to reduce immigration and the contentious dispute over the last government’s doomed effort to send some asylum seekers to Rwanda.

They were a particular target of the recent anti-immigrant riots, including in Rotherham, England, where a hotel housing some asylum seekers was attacked on Aug. 4, driving home the severity of the disorder.

Launched by a former prime minister, Boris Johnson, in 2022, the Rwanda plan was adopted as a flagship policy by Rishi Sunak, who entered Downing Street later that year. The courts ruled against the proposal, and despite months of political maneuvering, no asylum seekers were sent to Africa under the plan. After taking office, Mr. Starmer quickly scrapped the effort.

But Mr. Katwala said that by pledging to “stop the boats,” Mr. Sunak had drawn attention to the issue, sending “very loud messages” about how much control he would exert over national borders while delivering none. The result, Mr. Katwala said, was to “stoke up the level of concern over the issue, and completely fail on all fronts.”

By global standards the scale of small-boat arrivals is relatively modest and “the visible lack of control is much more the issue than the number of people coming via that route,” Mr. Katwala said.

While Mr. Starmer can try to lower the political temperature, his practical options for curbing English Channel crossings are limited. He plans to crack down on people-smuggling gangs, but, unless Britain strikes a new migration deal with France, recent experience suggests that step alone is unlikely to resolve the problem.

One thing the government intends to do is to speed up the system for processing asylum requests to cut the number of would-be refugees accommodated in hotels at public expense — a source of grievance to anti-immigrant protesters. (Asylum seekers tend to be accommodated in less wealthy areas where hotel costs are lower, making them a particular target in the recent riots.)

The fact that many more people have been allowed to enter the country legally has created another issue that has been weaponized by the far right, presenting Mr. Starmer with another big challenge.

Successive Conservative governments promised but failed to reduce annual legal net immigration to below 100,000, and control of the country’s frontiers was a key issue in a 2016 referendum in which Britons voted for Brexit.

Still, since Brexit, legal immigration has tripled, falling back only slightly from its 2022 peak — the highest on record.

Those figures were inflated by programs to accommodate people from Ukraine, Hong Kong and Afghanistan, for which there was wide public support. But Britain also relies heavily on foreign workers to fill jobs in health care and other sectors, and immigration is a driver of economic growth, so cutting it is hard.

“There is broad support for all the immigration that generates the very high numbers,” said Mr. Katwala, noting that most people welcomed Ukrainians and are happy for foreign workers to fill vacancies in British hospitals, “but then concern about the scale of the number.”

Before losing last month’s general election, Mr. Sunak tightened the migration rules, restricting the right of some legal immigrants to bring relatives to Britain. Those changes are expected to push down the numbers over the next year.

Reducing them further will be difficult without damaging health care and other key sectors, or impeding Mr. Starmer’s central objective of reviving the economy to ease Britain’s cost of living crisis. The recent unrest suggests that lifting economic growth, reviving neglected cities and investing in crumbling public services have never been more important.

The riots are “not telling this government anything it didn’t know,” Professor Fielding said. “They are just making its task more urgent.”

For travelers flying into the tiny island of Thitu, the reality of China’s territorial ambition becomes instantly clear. There they are: dozens of Chinese ships surrounding a speck of land that a few hundred Filipinos call home.

For now though, life is mostly peaceful and slow on the island. Small wooden fishing boats line a white sand beach on the eastern shore. Rough houses pieced together from plywood, scrap lumber and tarps are the main form of shelter. On a recent evening, a few people gathered near the beach to debone fish, while others waded into tide pools with fishing spears.

But the calm belies the fact that Thitu is contested land. Nearby, China has stationed a flotilla of coast guard ships and maritime militia vessels. On a neighboring reef, it has constructed a military base whose lights shimmer at night like a city. The intensifying Chinese presence has startled the Philippines, which has occupied Thitu for nearly half a century. So it is upgrading its crumbling military facilities that lie on the island’s southern end.

And it is encouraging more Filipinos to move in, betting more residents will strengthen its claim to Thitu, which it calls Pag-asa, or hope, and reduce hostilities with China.

These civilians are the only ones in the Spratly Islands — a chain of 100 or so atolls, reefs and cays in the South China Sea that may have significant oil reserves and is claimed by six countries. And they find themselves in the middle of a tense geopolitical dispute.

Marjorie Ganizo and her husband, Junie Antonio Ganizo, moved here with their eight children in November despite what they saw as the risk of a Chinese invasion.

“In the end, we had to ask ourselves: hunger or fear?” Ms. Ganizo, 36, said. “No matter where you are, if it’s your time to die, it’s your time to die.”

Tensions have flared between Beijing and Manila, which has a mutual defense treaty with the United States.

Two years ago, residents heard multiple blasts that jolted the island, and feared a war was breaking out. But the altercation — between Philippine and Chinese sailors, over falling debris from a Chinese space rocket — soon subsided.

In June, in another section of the Spratlys, a Chinese Coast Guard vessel rammed and punctured some Philippine military boats, severely injuring a soldier. Tensions have de-escalated in recent weeks, but even a small miscalculation on either side could trigger a conflict with global ramifications, as the South China Sea is a crucial waterway for international trade.

For the residents of Thitu, a stretch of roughly 90 acres of land, the Chinese blockade has narrowed their area for fishing, shrinking a key source of food.

But, for some, life is better here.

Mr. Ganizo now earns as much as $350 a month as a welder, compared with the $80 he made in Palawan, the Philippine province roughly 300 miles away that is closest to Thitu. The Chinese mainland lies more than twice as far to the northwest.

He is one of many civilians working on Thitu’s military facilities. Caught off guard by Beijing’s buildup in the region, Manila began upgrading the island’s facilities in 2018. It now has a sheltered port, years after town officials asked for it. Its once-muddy runway, usually unusable after light rain, has been upgraded to concrete. An aircraft hangar, a control tower, military barracks, health center and school building are under construction.

All supplies on the island — rice, flour, eggs, meat, livestock and medicines — have to be ferried in from the mainland. A lot of the food is given free to civilians, part of the lure of the island. But bad weather can thwart these supply trips and cause food shortages.

Until this year, there was no doctor on the island, and pregnant women are still required to move to the mainland for their third trimester. Electricity is available for a fee from a diesel power plant, but houses have no running water.

Sometimes it takes a certain kind of desperation to move to Thitu. Emmanuel Greganda came from Luzon, the country’s main island, in 2016, he said, to escape former President Rodrigo Duterte’s brutal war on drugs, which killed tens of thousands of people.

“I still wanted to live and change,” Mr. Greganda, 43, a former drug user, said while making wooden boat souvenirs outside his house. “My family and I were very scared because some of my friends were already killed.”

Like other male residents of Thitu, Mr. Greganda has been taught how to fire guns, to prepare for a Chinese incursion.

In 2021, Larry Hugo, the president of a fishermen’s group, was sailing to a sandbar near Thitu to fish when a big China Coast Guard ship blocked him, coming as close as 100 yards. Chinese ships regularly chase, shadow and drive away Filipino fishermen near Thitu and other parts of the South China Sea.

This June, a colleague and I spent five days on Thitu, after getting approval from the Philippine government. We flew in on a military plane and stayed with a family in their house facing the eastern shore, mostly eating fresh fish and other seafood. Last year, the government opened Thitu and other Philippine-occupied reefs and atolls in the Spratly Islands to tourists. Some residents have turned their houses into homestays for visitors.

More than 200 settlers, comprising about 65 families, live on the island. There are also about 150 workers brought here to upgrade the military facilities. Officials say roughly 100 soldiers, coast guard members and firefighters are stationed here.

While some experts say the presence of Filipinos in Thitu strengthens the country’s claim to the island, its mayor, Roberto del Mundo, said he was concerned about settlers freeloading.

“Many of them are abusing the generosity of the government,” said Mr. Del Mundo, a former air force soldier who was stationed on the island in the 1980s and 1990s. He recently cut the monthly food subsidy to only a few kilos of rice per person.

Still, many like Ms. Ganizo, the newcomer who was anxious about moving to the island, are happy to be here. Her children, including 13-year-old Jessa Mae, attend a school here, which now has 14 teachers catering to about 80 students. While some teachers are concerned that they don’t have the resources to prepare children adequately, others are thankful for jobs.

One recent evening, residents sang their hearts out on a karaoke machine, played billiards or basketball and drank alcohol. Many teenagers, glued to their smartphones watching TikTok and Facebook videos, hung out near the school for the free Wi-Fi.

Mr. Hugo, the fishermen’s group leader, moved to the island in 2011. He said the pace of life was perfect. “This is my home,” he said. “I’ll leave this island only when I’m dead.”

President Vladimir V. Putin of Russia lashed out at the West over Ukraine’s weeklong incursion into Russian territory, in a tense televised meeting with his top officials on Monday, a sign of how the surprise attack has unsettled the Kremlin.

Ukraine’s move has had two main goals, analysts said: to draw Russian forces from the front lines in eastern Ukraine and to seize territory that could serve as a bargaining chip in future peace negotiations.

Mr. Putin, speaking with security chiefs and regional governors at his residence outside Moscow, insisted that the attack would not soften his negotiating position. And even as Moscow scrambled to respond to the incursion into the Kursk region, Russian forces have continued to pummel Ukrainian forces in the east, Ukrainian military officials said on Monday. Mr. Putin’s statements projected confidence in Russia’s military position.

“The West is fighting us with the hands of the Ukrainians,” he said, repeating his frequent depiction of the 30-month war, which he started, as a proxy campaign against Russia by the West. “The enemy will certainly get the response he deserves, and all our goals, without doubt, will be accomplished.”

With his top general, Valery V. Gerasimov, seated a few feet away, Mr. Putin directed his military to push out Ukraine’s troops and to work with the border guard service to “ensure the reliable protection of the state border” — an acknowledgment that Russia had failed in that regard.

The Kursk region’s acting governor, Aleksei Smirnov, was shown telling Mr. Putin by video link that 28 towns and villages were under Ukrainian control. He said Ukrainian troops had pushed seven miles into Russian territory along a 25-mile front, that 12 civilians had died in the fighting and that 2,000 people were believed to be in Ukrainian-held territory.

His claims could not be independently verified, though the description of the extent of Ukraine’s advance roughly accorded with analysts’ estimates. On social media on Monday, the head of Ukraine’s armed forces, Gen. Oleksandr Syrsky, claimed control of more than twice as much territory, “about 1,000 square kilometers.”

While Russian civilians have previously been killed by Ukrainian shelling near the border, this is the first time that Ukrainian forces have seized a foothold in Russian territory. Mr. Smirnov said that 121,000 people had fled the border area, and that the authorities were working to evacuate another 59,000.

In interviews, some of the region’s residents said they were shocked at the turn of events, though there had long been speculation that Ukraine might attack.

“No one could have imagined it would come to a takeover,” said Natalia, 31, a manicurist in Zaoleshenka, a settlement near the border. She asked her last name be withheld for her safety.

Russian officials warned that Ukraine’s incursion could expand. In the neighboring Belgorod region, the authorities said they were evacuating the Krasnoyaruzhski border district, and that 11,000 people had already left. And Mr. Putin, in his televised meeting, told the governor of a third border region — Bryansk — that while it appeared “relatively calm” for now, “this doesn’t mean that the same situation will remain tomorrow.”

The incursion into Russia marked a significant shift in the war’s narrative.

Since launching their full-scale invasion in February 2022, Russian troops have expanded their hold to more than 18 percent of Ukraine. A Ukrainian counteroffensive last year failed; this year, the war has been mainly a slog in the country’s east, with Russian troops grinding forward sometimes a few feet at a time. Ukrainian morale has sunk, and pressure has built on Ukrainian leaders to negotiate a deal.

The incursion into Russian territory, far from the front line, was kept so secret that some Ukrainian soldiers and U.S. officials have said they did not know about it in advance.

There is little sign so far, however, that the shock is driving Russia to redirect frontline forces from eastern Ukraine. Instead of pulling those brigades, Russia appeared to be redeploying lower-level units to the Kursk region, according to a briefing on Sunday by the Institute for the Study of War, a U.S.-based think tank.

The analysis described the Russian force as “hastily assembled” and “ill-prepared” for a coordinated response.

Ukrainian troops along the eastern front line said they were still feeling pressure from the Russians.

“Our guys do not feel any relief,” said Artem Dzhepko, a press officer with Ukraine’s National Police Brigade, which is fighting near the strategically important town of Chasiv Yar in the Donetsk region of eastern Ukraine.

Russian forces there were still using as many as 10 aerial bombs a day, he said.

On Facebook, Ukraine’s military reported late Sunday that the Russian Army had tried four times to break through defenses along the front line at Toretsk, near the towns of Zalizne, Druzhba and Niu York. Two attacks were repelled; two were ongoing.

On Monday morning, the attacks near Toretsk continued, said Yevhen Strokan, a senior lieutenant and commander of a combat drone platoon in the 206th Territorial Defense Battalion.

“I don’t feel a decrease in intensity,” Mr. Strokan said. “Everything is being assaulted in the same way.”

The Kursk offensive, he said, might need more time to draw Russian troops away.

Alina Lobzina contributed reporting from London.

An 11-year-old girl and her mother, 34, were stabbed in London’s Leicester Square, a tourist hot spot, on Monday morning, the police said.

The victims were taken to a hospital, the police said in a post on social media, adding in a later update that the girl would require hospital treatment but that her injuries were not life-threatening. Her mother suffered more minor injuries.

The police said in a later statement that while they were continuing to investigate the suspect’s motive, “At this stage there is nothing to indicate the attack was terror-related.”

A 32-year-old man was arrested at the scene and was in custody, and the police said they did not believe there were any additional suspects. A video later emerged on social media showing police officers detaining the man, who was wearing a T-shirt with “Abbey Road” written on the front.

The episode came exactly two weeks after a deadly knife attack in Southport, near Liverpool, that led to the death of three young girls and injured eight other children and two adults. In the days after the stabbings in Southport, disinformation about the identity of the attacker, including a false claim that he was an undocumented migrant, spread rapidly online and ignited a series of violent riots around Britain.

In Leicester Square, an area in front of a shop called TWG Tea was cordoned off by blue and white police tape at 1:30 p.m., with a handful of police officers positioned at the scene. There were visible blood stains and a discarded baseball cap in the cordoned-off zone.

A man working as security in the tea shop said he had witnessed the attack and had intervened after a young girl and a woman he believed to be her mother were injured. Police officers then whisked the witness away for further questioning.

The BBC identified the employee as a 29-year-old named Abdullah. He told the BBC and the Press Association news agency that he had tackled the attacker, grabbing him and kicking the knife away before he and a few others held the man down until the police arrived. “I just saw a kid who was getting stabbed, and I just tried to save her,” he said in a video interview.

Two hours after the attack, hundreds of tourists continued to mill about the square. Shoppers at the Lego and M&M’s stores, which both frequently have long lines of people waiting to enter, craned their necks to see what was happening as a helicopter circled overhead.

Christina Jessah, a detective chief superintendent in charge of policing for Westminster, the central London borough containing Leicester Square, later paid tribute to workers from local businesses and members of the public who had intervened.

“They put themselves at risk and showed the best of London in doing so,” she said in a statement. She added that an investigation was continuing and the police were still working to establish what exactly happened.

“At this stage, we don’t believe the suspect and the victims were known to each other,” she said.

In a forest in western Ukraine, a few dozen young men and women stood at attention in two lines in the fading evening light. Some had fake guns slung over their shoulders.

Among them was Olesya Vdovych, who had spent the day with other members of the scouting organization Plast, hauling logs, running drills and learning about first aid as part of a two-week camp last August.

“I’m eager to be prepared,” Ms. Vdovych said at the time, her long blond hair tied in two braids under a forest green cap. With a number of her friends and family fighting in the war against Russia, she said she felt it was important to be ready for any situation.

For young Ukrainians like Ms. Vdovych, the once-carefree summers of childhood and young adulthood were forever altered by Russia’s invasion of the country more than two years ago. Since then, the war has ground on with little change in Ukraine’s fortunes, even as Ukrainian forces made a rare incursion into Russia last week, taking some territory, and engaging in furious fighting with Russian forces. Ukraine has struggled to hold back Russian forces in the east, and devastating airstrikes continue to bombard cities far from the front lines. In April, Ukraine lowered the draft age for young men, to 25 from 27.

Against this backdrop, scouting camps like the one run by Plast have taken on a new resonance. Traditions like hiking and campfires, intended to foster an appreciation for nature, have been supplemented by activities with a more patriotic tone. New camps have also sprung up, some intended to prepare youngsters for battle, with a focus on team-building, first-aid skills and military preparedness.

Some camps are run by the youth branches of right-wing groups with a distinctly nationalistic bent as they take on the mission of molding future Ukrainian soldiers. And some have intensive — sometimes punishing — physical challenges.

This year, Ms. Vdovych will return to the Plast camp in the forest, this time as an instructor leading scouts ages 15 to 21 through the same exercises she did last year.

“There is no question of if I will go to war,” said Ms. Vdovych, 20, reflecting recently on the camp. “It’s not if, but when.”

“Everyone has to be involved and ready,” she added.

Plast, founded in 1911 in western Ukraine, has roots in the global scouting movement started by Robert Baden-Powell, a British lieutenant general.

The group was officially banned for decades as Polish, German and Soviet forces controlled the area, said Olga Svinzinska, a historian and Plast member who is an authority on the group’s history. Still, it thrived within the Ukrainian diaspora and among those who pushed for an independent state. Plast was revived when the Soviet Union collapsed and the Ukrainian state was founded in 1991.

Interest in the group grew with a surge in patriotism after the 2014 Maidan uprising, which toppled a pro-Russian leader and led to the Russian-backed separatist conflict in eastern Ukraine. Dozens of former Plast scouts have volunteered in the struggle, according to the organization, and at least 58 have been killed since the fighting began.

Ksenia Dremliuzhenko, a chairman of the regional Plast council, said she had seen a noticeable shift in the mood of scouting camp participants in the past year, reflecting the challenges of the war with Russia.

“Everyone feels this fatigue, but there is an understanding of what we are fighting for,” she said. “We cannot give up when our friends have already died for our freedom.”

Many of the camps are rich with symbolism and infused with folk tradition.

At a Plast camp aimed for scouts ages 15 to 20, in the Lviv region, participants wear vyshyvankas — the intricately embroidered shirts of the country’s national dress — as they recreate Kupala Day, a Ukrainian folklore crowning ceremony.

These days, the camps have also taken on an additional role as war upends Ukraine’s educational system. Thousands of schools across the country have been damaged or destroyed, and many students have fled the country with their families. In schools where in-person classes have continued, ongoing airstrikes regularly send students scrambling for shelters.

“The war has a great impact on children,” said Ivan Svarnyk, a historian and educator, “when missiles are flying, when bombs are falling, when their friends are dying, and this is a huge test for the child’s psyche.”

For many, playtime has ended, Mr. Svarnyk added. Others are finding the war makes its way into their games.

Last summer, on the road to Kharkiv, in Ukraine’s northeast, three young children played checkpoint, mimicking blockades set up around the country by the military. During their summer break from school, they stood outside for hours, wearing camouflage and mock uniforms, carrying two knives, binoculars and a toy pistol, and proudly displaying the Ukrainian flag.

Summer camps also offer an escape from the realities of war.

At the Hedgehog’s Camp for the youngest Plast members, children ages 3 to 6 spent a week last August in the forested mountains of the Lviv region. The camp took the children on a woodland adventure through storytelling of Ukrainian folklore and mythology, woven with an appreciation of nature.

The adults running the camp wore costumes depicting characters from these ancient stories, while the children ran through the leafy mountain trails, far from the thoughts of air raid sirens and frontline fighting.

But the war is never really far. Some of the children had been displaced from their homes, forced to flee across the nearby border in Poland and return only sporadically. One of the campers, Marko, 5, attended the camp with his mother, Vira Ihorivna, 33. His father was a volunteer soldier and was killed fighting in the east.

“He understands, but probably as a child, that his father is dead,” Ms. Ihorivna said.

Older scouts must grapple with the idea that they may eventually take the lessons they learn at camp to the front lines.

“I understand that although many people hope that the war will end quickly — you need to believe in the best — but you need to be prepared for everything,” said Ms. Vdovych, the scout at the camp who will return as an instructor.

Out in the forest, where scouts can count only on themselves, she said that lesson on preparedness had been drilled home, along with the idea “We can only count on ourselves.”

“Learning how to build your little life in nature will make it easier in real life,” she said, adding: “There are always challenges. But you learn how to deal with storms and unexpected turns.”

Diego Ibarra Sanchez and Anna Ivanova contributed reporting.