Ukraine has asked to use Western long-range weapons to strike deeper into Russia for months. It argues that it needs those weapons to hit military sites that house Russian warplanes and that launch missiles into Ukrainian cities.

Those entreaties were a major topic of discussion on Friday as President Biden met with Prime Minister Keir Starmer of Britain, who is trying to nudge the United States to give more latitude to the Ukrainians. Mr. Starmer would especially like Mr. Biden’s support for Britain to allow Ukraine to use British Storm Shadow missiles to fire farther into Russia.

Neither leader announced any policy changes after that meeting. Leaving the White House, Mr. Starmer told reporters, “We had a wide-ranging discussion about strategy,” and a White House summary of the meeting said that the two countries had “reaffirmed their unwavering support for Ukraine.”

Mr. Biden has been reluctant to approve deep strikes in the past, fearing escalation with Russia. But in May, he allowed Ukraine to fire a number of U.S.-supplied weapons just over the border to attack Russian military bases from which attacks into Ukraine have been launched, and he later expanded that permission.

Now, Ukraine wants long-range weapons. It is also seeking permission to use weapons it already has to hit targets deeper in Russia. President Vladimir V. Putin of Russia warned on Thursday that if the United States and its allies allowed that, they would put his country “at war” with NATO.

The debate in the U.S. administration centers, in large part, on these weapons.

Storm Shadows and SCALPs

Britain and France have already sent Ukraine air-launched cruise missiles that, so far, have struck Russian targets in Crimea and in the Black Sea. These missiles have a range of about 155 miles and have been fired from Ukraine’s aging fleet of Soviet-era and Russian-designed fighter jets.

They are known as Storm Shadows in Britain and SCALPs in France (and are virtually the same model).

Britain is eager to allow Ukraine to use the Storm Shadows to strike farther into Russia. Mr. Starmer was hoping to receive Mr. Biden’s approval of that plan so the allies could present a united front.

France has previously expressed support for Ukraine’s deep strikes into Russia, but only on military targets directly linked to Moscow’s war efforts in Ukraine.

Some analysts expect the United States to follow a pattern it established with Ukraine’s previous requests for weapons, like Abrams tanks, F-16 fighter jets and Patriot air defense systems: After long deliberations, Washington eventually allows its allies to move first in providing Ukraine with new capabilities or permissions, and then sometimes follows suit.

ATACMS

The Army Tactical Missile Systems, known as ATACMS (pronounced “attack ’ems”), are American-made long-range missiles that are filled with 375 pounds of explosives and, depending on the model, can strike targets up to 190 miles away. The United States supplied Ukraine with ATACMS last year, but the Biden administration has so far withheld its approval for their use across the border into Russia.

Russia has now moved 90 percent of its air bases that house bomber jets out of ATACMS range, U.S. and European military officials said, in anticipation that Ukraine could soon be allowed to fire the missiles across the border.

Originally developed in the 1980s to destroy Soviet targets far behind enemy lines, ATACMS could also strike Russian ground-based air-defense systems that target Ukraine’s newly furnished fleet of F-16s, experts said.

JASSMs

Joint Air-to-Surface Standoff Missiles, or JASSMs (pronounced “jazz ’ems”), are air-launched cruise missiles with a range of about 230 miles. These have not yet been provided to Ukraine, but a U.S. official said that the Biden administration was considering sending them.

The weapons carry 1,000-pound warheads and can be fired from F-16s. This means that with JASSMs, Ukraine could strike military targets well within Russian territory without leaving Ukrainian airspace.

Ukraine is believed to have received around a dozen American-made F-16s this summer, though officials have not said exactly how many.

The U.S. official said that even if Mr. Biden approved sending JASSMs to Ukraine, delivery might take months, and it is unclear whether Mr. Biden would allow Ukraine to fire these missiles into Russia.

Eric Schmitt and Aurelien Breeden contributed reporting.

After racing across Russian fields in an American Stryker armored fighting vehicle this month, the six-man Ukrainian assault team dismounted in a tree line about 700 yards from the enemy’s trenches and waited for the order to attack.

When it came, Afonya, a 40-year-old construction worker drafted into the Ukrainian military just two months ago, said the Ukrainian soldiers were met with a hail of gunfire as soon as they moved from their hastily dug foxholes. He was hit in the hand by a bullet that shattered a bone.

Three members of the assault team were injured and pulled back while the other three waited for reinforcements to resume the attack in the Kursk region of Russia.

“There were too many of them,” Afonya said in an interview at a hospital in eastern Ukraine, where he was recovering after being evacuated.

More than a month after Kyiv launched its incursion into Kursk — sweeping across nearly 500 square miles and capturing around 100 Russian towns and villages in a few short weeks — Russian resistance is stiffening, Ukrainian soldiers interviewed near the border with Russia said as they moved to and from the front last weekend.

President Volodymyr Zelensky told reporters on Thursday that Russian forces had begun a concerted counterattack in Kursk.

Some of the heaviest battles have been taking place on the western edge of the new front, according to the soldiers and combat footage geolocated by military analysts. But the battle lines remained fluid, and there was little reliable information about the scale of Russia’s operation or how successful it has been in reclaiming territory.

Ukrainian soldiers said that even as Russia was counterattacking in some locations, they remained on the offensive along other parts of the Kursk front. But their advances have slowed and clashes are growing deadlier as Moscow deploys reinforcements and increases its aerial bombardments.

“There is more resistance,” said Yurii, 21, who was with one of the first Ukrainian units to cross the border when the incursion was launched on Aug. 6. There are more drones, “more shells, and even anti-tank guided missiles,” he said. “Their intelligence is also working very hard. As soon as a vehicle moves out, their artillery starts firing immediately.”

The Ukrainian soldiers spoke on the condition that only their first names be used, in accordance with military protocol. They also asked that their brigades not be named out of concern that it could give the Russians insight into the location of their forces.

While some of the information they provided is corroborated by geolocated combat footage, details about specific offensive movements could not be independently verified.

As powerful Russian guided bombs thundered in the distance on a recent day and a puff of smoke overhead marked the spot where a Russian surveillance drone was shot out of the sky, one group of soldiers, speaking on the side of a road near the border, said that more Russian troops were joining the fight every day.

Dmytro, a 40-year-old member of a drone unit, said the fighting in Kursk was still less intense than other battles he has fought in over the course of the war, but that is changing.

“They’re trying, but so far, nothing’s working for them,” he said. “We are still attacking.”

The soldiers said that much of the fighting before the Russian counterattack was for small tactical advantages — like taking control of a ridge or hill — that could prove useful in future battles.

Ukraine is using new forward positions inside Russia to disrupt Moscow’s logistical operations, attacking roads and bridges along critical supply lines feeding Russian forces inside Ukraine, soldiers said.

And they are continuing efforts to isolate a large group of Russian soldiers in a 270-square-mile pocket of land between the Ukrainian border and the meandering Seym River about 10 miles inside Russia, they say.

Ukrainian forces destroyed all of the bridges across the river and are targeting temporary pontoon bridges as soon as they are spotted, according to soldiers, satellite imagery and geolocated combat footage. But the Russian counterattack this past week appeared designed to relieve pressure on that pocket of land.

Russia’s Defense Ministry said its country’s forces had “penetrated” into the Kursk region, capturing 10 settlements.

The Institute for the Study of War, whose analysts use geolocated combat footage to track daily battlefield developments, wrote on Friday that they had yet to observe visual confirmation to support the Kremlin’s claims, with Russian soldiers appearing to be in partial control of two villages.

At the same time, Ukrainian forces breached the border in a new location west of the original incursion, according to combat footage released by both sides and geolocated by military analysts. The state of the fighting there is unclear, but it could complicate Russia’s counterattack.

As they battle to hold onto their gains, the Ukrainian soldiers said the campaign was coming at a steep cost.

“Every centimeter of our advance costs human lives,” said Serhii, a 40-year-old Ukrainian soldier whose home village, Sumy, is close to the Russian border.

The Kremlin is clearly hoping the Ukrainian military has overextended itself, leaving outnumbered and outgunned Ukrainian forces in the country’s eastern Donbas region vulnerable as Russia continues to press the attack there, military analysts say.

President Vladimir V. Putin has sought to minimize the first invasion of Russia since World War II as a mere distraction. While saying it was a “sacred duty” to expel Ukrainian forces, he said Russia’s main priority remained seizing Ukrainian lands.

Mr. Zelensky and Ukraine’s top military commander, Gen. Oleksandr Syrsky, have said the offensive has multiple goals, including drawing Russian forces from other parts of the front.

While the Ukrainian leaders acknowledged that the Kremlin has resisted pulling its best forces from the hottest parts of the eastern front as they had hoped, General Syrsky has maintained that the Kursk offensive is still affecting Russia’s ability to sustain other operations around the battlefield as it moves some 60,000 soldiers to the Kursk front.

Bill Burns, the C.I.A. director, told a conference in London last weekend that the operation was “a significant tactical achievement” that had boosted Ukrainian morale and exposed Russia’s weaknesses.

Mr. Zelensky has said the offensive is a part of a “Victory Plan” that he will present to President Biden and the two candidates vying to replace him — Kamala Harris and Donald J. Trump — on a trip to the United States this month.

Whatever the ultimate plan, Kursk is now clearly another violent front in an already sprawling war.

“Same war, different place,” said Dmytro, the drone operator.

As the Russians fight to halt the Ukrainian advance, soldiers said, they are using the same tactics they use inside Ukraine — a scorched-earth approach that has left dozens of Ukrainian towns and cities in ruins.

But the Russian bombardments are now devastating Russian homes, soldiers said.

“I bring the guys food, fuel, diesel, and gasoline over there,” a 56 year-old soldier who works in logistics, also named Serhii, said at a rest stop on the Ukrainian side of the border. “It was strange, when our troops first came, everything was intact. The roads were fine, the warehouses were untouched.”

“But after a couple of weeks, everything was destroyed, shattered,” he said. “They are destroying their own villages.”

Those claims by the Ukrainian soldiers were supported by combat footage showing Russian strikes on Russian villages and towns occupied by Ukrainian soldiers.

In Sudzha, the largest town under Ukrainian control, some high-rise and administrative buildings were destroyed as the Ukrainians advanced, but independent Western journalists who visited the region in the first days after it fell noted that the level of destruction was minimal compared with places in eastern Ukraine seized by Russian forces.

That is fast changing.

“Now, when you stand on a hill, for example, and look at Sudzha, you wake up every morning thanking God that you’re alive,” said Serhii, the soldier from Sumy. The town, he said, is a “land on fire.”

As he prepared to head back into Russia at nightfall, he said his heart was heavy with emotion. He understood the mission and thinks it is important, but would rather not have to fight on foreign soil.

“It’s one thing to defend your own land, but another to be over there,” he said.

Liubov Sholudko contributed reporting from eastern Ukraine.

Paris threw its last Olympics party on Saturday, a buoyant, nostalgia-tinged celebration of the 2024 Games that drew tens of thousands of cheering spectators to the streets of the French capital for a parade of athletes and an outdoor concert around the Arc de Triomphe.

The festivities started with smoky blue, white and red fireworks, echoing the start of the opening ceremony on the Seine. Flag-waving crowds then roared and sang France’s national anthem as more than 300 French Olympic and Paralympic contestants paraded up the Champs-Élysées on a giant white runway.

“Thank you all,” Teddy Riner, the French judo legend, told ecstatic spectators as they sounded air horns and chanted athletes’ names. “It was incredible!”

Medal-winning athletes were later decorated with state honors, some of them by retired French sports legends, and a handful were honored by President Emmanuel Macron himself. France won 64 medals, putting it in the top five of the Olympics medals count. And it earned 75 medals at the Paralympics.

After night fell, the Olympic cauldron floated into the air one last time and a highlight reel of the Games was projected onto the Arc de Triomphe. Performers from the opening and closing ceremonies also returned for an encore on a ring-shaped stage around the famous monument (including Philippe Katerine, a.k.a blue Smurf guy). French fencers, rugby players and others led the concertgoers through giant karaoke sessions.

It was a day of summer revelry before the fall doldrums set in, the end of an Olympic bubble that enchanted France and allowed it to forget, for a time, its current political turmoil and a looming government budget crunch. It was also a final opportunity to watch the Phryges, the widely beloved mascots of the Paris Games, in all their googly-eyed glory.

“We rose to the challenge and it went very well,” said Marie-Laure Bordes, 48, peeking from the back of the crowd to catch a glimpse of the Champs-Élysées, where thousands of volunteers and staff members from the organizing committee also paraded to widespread applause. She cited the smooth organization and euphoric mood as her family’s highlights of the Games.

“And Léon Marchand!” her teenage son said, referring to the French swimming superstar,

“Now that it’s over,” Ms. Bordes added, “there is a feeling of nostalgia.”

Spectators said they rushed to snap up the free tickets to the event, largely to relive the unexpected unity and fervor that gripped Paris during the Games after months of hand-wringing about whether France would be ready — and enthusiastic enough — for the Games.

“France is a grumpy place,” said Maryline Bregeon, 63, a retiree who volunteered at the opening ceremony and at the horseback riding events at Versailles. But the mood shifted noticeably during the Games, she said on the sidelines of the parade, wearing her official turquoise volunteer jersey.

“People were talking to each other on public transit,” she marveled. “Usually that never happens.”

France’s leaders are keen to capitalize on that spirit.

Anne Hidalgo, the mayor of Paris, wants to keep the Olympic rings on the Eiffel Tower, at least until Los Angeles hosts the 2028 Summer Games, although her plans have run into opposition.

Mr. Macron wants to make Sept. 14 a national day to celebrate sports. Weakened politically after inconclusive snap elections and forced to appoint a conservative prime minister who is not from his party, the French president has tried to portray the Games as an example of much-needed national unity.

“Who could understand that we know how to reach out and surpass ourselves to make the Olympic and Paralympic Games a success, but that we can’t do the same to build France and respond to the urgent needs of the French people?” Mr. Macron told Le Parisien, a newspaper, on Friday.

Mustapha Belfodil, 33, an Algerian doctor who works in Grenoble, in the French Alps, said he had taken a week off to volunteer as a medic at the track and field events — and had no regrets.

“I wanted to relive these moments,” he said at the parade, citing the victories by Mr. Marchand and the triumph of Imane Khelif, the gold-medal-winning Algerian boxer, as among his favorites.

But in the end, he said, “there were too many to choose from.”

Prime Minister Justin Trudeau’s Liberal Party should be a shoo-in for a Parliamentary seat at the southern point of the island of Montreal.

The district has been a stronghold for his party for more than half a century. It was home to another Liberal prime minister a generation ago. The base for a former Liberal justice minister. An easy drive to Mr. Trudeau’s own redoubt in the city.

And yet, days before a special election on Monday to choose the district’s member of Canada’s Parliament, polls show a tight three-way contest. For many lifelong Liberals, the problem is clear: It is Mr. Trudeau himself.

“I am a Liberal supporter, but it’s almost like enough is enough,” Michael Altimas, 79, a retired city bus driver, said during a walk on a sunny day along the district’s long pedestrian commercial street. “For the most part, he’s been a good prime minister.”

“But he’s had nine years,” Mr. Altimas added, “and people are hearing often enough that he messed up and they don’t want to support him anymore.”

The election to fill a vacancy in the district has become a referendum on Mr. Trudeau, the once golden boy of Western leaders who is now fighting for his political survival. His own Liberal Party members are increasingly calling for him to step aside, worried that the party risks a drubbing in the next general election under the deeply unpopular leader.

Public grumblings about his leadership grew louder over the summer after his party lost a special election in Toronto in June — in another stronghold — and after President Biden’s decision to step down as the Democratic candidate in the U.S. election suggested a path forward for Canada’s Liberals.

The stunning loss in Toronto has raised the stakes for the election in Montreal. Underscoring Mr. Trudeau’s cratering popularity is his near total absence from the local campaign.

His face does not appear on posters in the Liberal campaign office’s storefront windows or on the district’s lampposts. He appeared once to introduce the Liberal candidate, but hasn’t been back since. Other party leaders, by contrast, have been visibly present.

“Right now, Justin Trudeau has no political coattails,” said Nik Nanos, a leading pollster in Canada. “He’s become the lightning rod for the general disaffection directed at the Liberal Party.”

When Mr. Trudeau was first elected in 2015, he enjoyed “one of the strongest brands in the polling history of Canada,” Mr. Nanos said. But Mr. Trudeau’s approval ratings are now stuck just above 20 percent and trail by double digits those of the main opposition Conservative Party leader, Pierre Poilievre.

For the past year, Mr. Poilievre has set the national political agenda through relentless attacks on Mr. Trudeau’s handling of issues most concerning to voters, including the economy, housing and immigration. The Liberal government has often reacted to Mr. Poilievre’s criticisms with hurried policy tweaks.

Mr. Trudeau has vowed to run for a fourth term in the next general election, which must be called by the fall of 2025. But a string of recent developments has amplified the pessimism of Liberals and former allies: the abrupt resignation of the Liberal Party’s campaign director; the labor minister’s resignation and the transportation minister’s public angling for a provincial post; an exodus of senior government employees; and the sudden decision by the New Democratic Party to abandon an agreement to support Mr. Trudeau’s party for fear of being tainted by the association.

A loss in Montreal’s special election could embolden internal opposition and further undermine Mr. Trudeau’s public image.

The district, called LaSalle–Émard–Verdun, has been redrawn a few times but has been a Liberal fortress since the 1960s. Its traditionally working-class and immigrant residents backed the Liberals, as have newcomers to its gentrifying neighborhoods.

In the last general election in 2021, the Liberal candidate won by 20 percentage points over his closest rival. Today, polls show the Liberals with a slight edge but locked in a tight battle against two opposition parties, the Bloc Québécois, a national party that supports Quebec independence, and the New Democratic Party.

Many voters interviewed on Wellington Street in Verdun — a long pedestrian street filled with restaurants, cafés and neighborhood stores — singled out Mr. Trudeau for influencing their decision.

“It’s hard to imagine a world in which Trudeau gets re-elected,” said Christopher Gaudreault, 28, a classical pianist, who has voted for Liberals, Greens and New Democrats. “What I’ve been hearing in my circles is that pretty much everyone across the board is fed up with Trudeau for various reasons.”

“People are just eager for a change and hope for something better,” he added.

So far, Mr. Trudeau has wielded the extraordinary powers conferred on Canada’s political party leaders to quash internal dissent.

Last November, Percy Downe, a Senator who served as chief of staff to a former prime minister, became one of the first Liberals to suggest publicly that Mr. Trudeau step aside for a fresh face before the next election. Few Liberals followed suit — at least publicly.

Mr. Downe, in an interview, explained that most senators — who, under Canada’s Constitution, are appointed rather than elected — have been named by Mr. Trudeau. At the same time, the more powerful members of the House of Commons fear questioning Mr. Trudeau, who, like all Canadian party leaders, enjoys near total control over individual party members’ electoral prospects.

“You won’t be allowed to run in the next election,” Mr. Downe said, pointing out that no candidate can run in a district without the party leader’s endorsement. He called party leaders’ absolute power over their members “a fundamental weakness in our democratic system.”

After the Liberals’ loss in the Toronto race in June, the Canadian news media was filled with anonymous Liberal criticism of Mr. Trudeau’s leadership. Only one Liberal member of Parliament — who has announced that he was retiring from politics — openly called on Mr. Trudeau to step down. Other Liberal lawmakers called for an emergency national meeting to discuss the party’s future.

Mr. Trudeau brushed away those calls.

Royce Koop, a political scientist at the University of Manitoba, said Mr. Trudeau had succeeded because time was running out for the Liberals to change leaders before the next election.

“If you’re Trudeau and you’re trying to hang on, delay is a good tactic,” Mr. Koop said.

Even though Mr. Trudeau has largely stayed away from the LaSalle–Émard–Verdun race, his grip on the party is still evident. Mr. Trudeau handpicked the candidate, a city councilor named Laura Palestini, in mid-July — angering three other Liberal candidates vying for the candidacy.

One of them, Christopher Baenninger, an entrepreneur, said Liberal Party officials had reassured him that the candidate would be elected by members in an open race. He said he had spent five months gathering support, knocking on doors seven days a week.

Among Liberal supporters, he said half were committed “no matter what.” But he said the other half were “tired Liberals, who were, like, ‘Trudeau’s been in power for nine years now. We’re looking for something fresh.’”

The open nomination had made Liberals “feel like their voices are heard,” said another former candidate, Eddy Kara, a Liberal organizer and a filmmaker. But the last-minute decision to close the nomination and parachute in a candidate risks leaving Liberals feeling disenfranchised and “exacerbating people’s negative perceptions” about politics, he added.

Parker Lund, a Liberal Party spokesman, said in an email that the selection of Ms. Palestini was “fully in line with our national nomination rules.” He did not respond to requests to interview a senior party official about the state of the Liberal Party.

At Ms. Palestini’s campaign office, the campaign manager, Marie-Pascale Des Rosiers, said the candidate was not granting interviews and declined to let a journalist accompany her while campaigning.

A few doors away, at the New Democrats’ campaign office, the excitement about a possible upset victory was palpable. The party’s leader, Jagmeet Singh, whose own electoral district is in a Vancouver suburb, has visited Montreal about a dozen times to campaign with the party’s local candidate, Craig Sauvé, a city councilor.

The Bloc Québécois, whose candidate is Louis-Philippe Sauvé, has also expressed optimism about winning.

The New Democrats’ candidate, Mr. Sauvé, said he was knocking on doors two to three times a day.

“There is a generalized fatigue,” he said, “with regards to the Liberal Party.”

Abbé Pierre, a Roman Catholic priest who crusaded against homelessness in France, is such a celebrated figure in the country that television viewers once voted him the third-greatest French person of all time. Streets, schools and public parks are named for him. He was seen as a steady moral compass for the nation, even after he died at age 94 in 2007.

But over the past two months a much darker image has emerged: that of an accused sexual predator.

Years after his death, Abbé Pierre is facing a sudden profusion of sexual harassment and assault accusations — a stunning fall from grace that has prompted soul-searching at the social justice movement he started; raised uncomfortable questions about who knew about his behavior toward women; and unsettled a country that once hailed him as a symbol of virtue.

“The image of purity, of solidarity, of empathy that he had is crumbling,” said Axelle Brodiez-Dolino, a historian at France’s National Center for Scientific Research who has written a book about Abbé Pierre and Emmaüs, one of the nonprofit organizations that grew out of the movement he founded to address poverty and homelessness.

“That doesn’t change the good that he did in the past,” she added. “But there was a dark side to him that the broader public was completely unaware of.”

Two reports, commissioned by the nonprofits and published in July and this month, have laid bare accusations that Abbé Pierre sexually harassed or assaulted at least two dozen women between the 1950s and the 2000s, mostly in France but sometimes abroad, including in the United States. The accusations have been made by the women themselves, by members of their families, or by witnesses.

One woman said Abbé Pierre groped and kissed her when she was 8 and 9 years old in the mid-1970s. Another said he forced her to watch him masturbate and to perform oral sex on him in 1989. Yet another said Abbé Pierre abused her after she asked for help finding housing in the early 1990s.

The reports do not publicly identify anyone who came forward, but say the accusers were nonprofit employees or volunteers, members of families close to him, staff members at establishments he visited or people he met through his charitable endeavors.

The reports were compiled by Groupe Egaé, a private consulting firm that specializes in preventing sexual and sexist violence. It conducted an investigation at the request of the nonprofits — the Abbé Pierre Foundation, Emmaüs France and Emmaüs International — after a woman came forward privately in 2023, accusing the priest of sexual assault. The organizations say they believe the accusers and expect more to come forward.

“Our movement knows what it owes to Abbé Pierre,” the organizations said in a joint statement. “Now, we must also confront the unacceptable suffering that he forced upon others.”

Abbé Pierre, born Henri Antoine Grouès in 1912 into a wealthy silk-merchant family from Lyon, entered a Capuchin monastery at age 18. He fought with the French Resistance during World War II, served as a chaplain in the French Navy and became a lawmaker.

He campaigned for the homeless, issuing a famous radio call for shelter and supplies during the harsh winter of 1954. That effort inspired a 1956 law that is still in effect in France, making it illegal to evict tenants during the coldest winter months.

After that, not even the occasional brush with controversy dented his national image. He topped a newspaper ranking of France’s most popular personalities 17 times.

Now the nonprofits he left behind are scrambling to distance themselves from a man who was inextricably linked to their work. While he was rarely involved in the day-to-day running of their operations, his scruffy beard, black beret and cape made him an instantly recognizable advocate.

The Abbé Pierre Foundation said that it was going to change its name. Emmaüs France said it would move to remove his name from its logo. An independent commission of experts will investigate how he was able to act unimpeded for more than half a century.

“What we are trying to do through these measures isn’t to forget Abbé Pierre or obfuscate his role,” said Adrien Chaboche, the chief executive of Emmaüs International. “What we are changing is the way that we, as a movement and as associations, present ourselves to the world — and we can’t do that with a figurehead who now embodies such a disgraceful and reprehensible reality.”

They are not the only ones reassessing his legacy. Some cities in France have said they would be stripping his name from public spaces. Nancy, in the east, said it would remove a plaque honoring Abbé Pierre that was affixed only months ago.

How much of his behavior was known to those close to him is unclear. The reports, and investigations in the French news media, suggest that some people close to him knew he had a problematic attitude toward women.

Some victims had alerted nonprofit colleagues or managers of the abuse, the reports said. One charity worker cited said female colleagues were advised not to meet with Abbé Pierre alone. And Martin Hirsch, who was president of Emmaüs France from 2002 to 2007, wrote in a newspaper in July that it was an open secret within the organization that he had once been sent to a psychiatric clinic in Switzerland “because his attitude toward women was problematic.”

Abbé Pierre had publicly confessed later in his life to having sexual relations with women as a priest. But years before the #MeToo movement and broader scrutiny of sexual abuse in the Roman Catholic Church in France, the focus appeared to have been more on whether he had broken his vows — and less on whether those relations were consensual.

Pope Francis said on Friday that he did not know when the Vatican had learned about the abuse but added that “certainly after his death, it became known.”

“Abbé Pierre was a man who did a lot of good but was also a sinner,” the pope said on the plane returning from a trip to Southeast Asia and Oceania. “We must speak clearly about these things and not hide them.”

Agnès Desmazières, a historian who has written a book about sexual abuse in the Catholic Church, drew a parallel with the case of Jean Vanier, the Canadian founder of a French charity who was accused after his death of engaging in several abusive sexual relationships.

Mr. Vanier and Abbé Pierre were both charismatic figures admired for their charity work, she said. Each has since been accused of using that reputation to abuse women.

“In a way,” Ms. Desmazières said, “Abbé Pierre’s charitable success protected him.”

Ségolène Le Stradic contributed reporting.

One is a colossus spanning theme parks, merchandise and movies, with 150 Academy Awards, 225,000 employees and annual revenue of nearly $90 billion.

The other is a third-generation family firm with 280 workers that packages hot sauce, soy beans, multicolored sprinkles, a herb called horsetail, six varieties of panettone and seven kinds of salt for sale in Paraguayan supermarkets.

Yet Mickey (MEE-kay) is a household name to rival Disney across the little-touristed South American nation of 6.1 million. In fact, a visitor might assume they’re partners.

There are the red uniforms worn by Mickey’s staff. There’s its family-friendly slogan: “the obligation to be good!”

Above all, there’s the cartoon mouse — also called Mickey, and indistinguishable from Mickey Mouse — whose iconic circular ears adorn the gates of the company’s factory, its trucks and a mascot in heavy demand at Paraguayan weddings.

But don’t get it twisted, said Viviana Blasco, 51, sitting in the capital, Asunción, among Mickey-branded stationery, T-shirts, and coffee cups.

There’s “the Disney Mickey,” said Ms. Blasco, one of five siblings who run the business, and “the Paraguayan Mickey, our Mickey.”

Still, if the Paraguayan Mickey seems remarkably similar to the Disney one, it may not be entirely a coincidence.

Paraguayans are notoriously creative — some would say light-fingered — when it comes to intellectual property.

Factories churn out knockoff Nike, Lacoste, and Adidas clothing. Paraguay’s educational authorities warned last year that Harvard University Paraguay — in Ciudad del Este, the country’s second-largest city and a counterfeiting hot spot — was awarding bogus medical degrees. (The school has no connection to the more famous Harvard.)

Paraguay ranks 86th out of 125 countries in an index compiled by the Property Rights Alliance, a research institute based in Washington, scoring 1.7 out of 10 for copyright protection.

But Mickey, the Blasco family enterprise, has survived multiple legal challenges leveled by Disney.

It is also a remarkably beloved institution that speaks to Paraguay’s peculiar history, gastronomy and national identity.

The Mickey saga began, Ms. Blasco said, in 1935.

Paraguay had just endured a deadly conflict with Bolivia over the Chaco, a tangle of sun-baked scrub. An earlier conflagration, the War of the Triple Alliance (1864-70), had seen Argentina, Brazil and Uruguay wipe out half of Paraguay’s population.

It was still reeling from both.

Ms. Blasco’s grandfather, Pascual, the son of Italian immigrants, saw an opportunity to spread some joy — and turn a profit. He opened a tiny shop selling fruit and homemade gelato. It was called Mickey.

Exactly where the idea came from, said Ms. Blasco, remains “something of a mystery.”

But Pascual, she said, often vacationed in Buenos Aires — Argentina’s cosmopolitan capital, known for movie theaters showing international films. Mickey Mouse was making his silver-screen debut, including in “The Gallopin’ Gaucho” (1928).

“On one of his trips, he must have seen the famous mouse,” Ms. Blasco said.

Whatever its origins, Mickey was a hit. A few years later, Pascual opened the Mickey Ice Cream Parlor, Café and Confectioners.

By 1969, Mickey was selling rice, sugar and baking soda in packages now decorated with the eponymous mouse. In 1978, the business moved to a factory topped by a 62-meter illuminated Christmas tree.

Ms. Blasco denied that her family had appropriated Disney’s property.

“We didn’t take it, we built a brand over many years. Mickey grew in parallel to Walt Disney,” Ms. Blasco said, becoming “deeply implanted in Paraguayan culture.”

That affinity was evident at several stores that stock Mickey products in Luque, a working-class suburb of Asunción.

The Mickey mascot was taking photos with fans, including Lilian Pavón, 54, a pediatric nurse. “I’m a fanatic of Mickey products,” she said, praising, in particular, the company’s breadcrumbs and oregano.

But her feelings for the 7-foot felt rodent go beyond condiments, she added, as Mickey bumped fists with shoppers and distributed ring-shaped biscuits called chipa.

As children, she said, she and her friends hoarded Mickey Mouse pencil cases, notebooks and stickers. They dreamed of visiting Disneyland or Walt Disney World. But the cost of flying to Anaheim or Orlando made the pilgrimage “impossible,” even as an adult, Ms. Pavón said.

“I’m happy just to see Mickey in places like this,” she added, standing in the chilled meats aisle of El Cacique, a budget supermarket.

Mickey resonates with Paraguayans’ sense of nostalgia, said Euge Aquino, a TV chef and social media influencer who uses its ingredients to make comfort food like pastel mandi’o (yuca and beef empanadas).

Paraguay is not known for its haute cuisine, she admitted.

It’s flat, hot, and a long way from foreign foodie trends.

“Our climate is pretty difficult,” Ms. Aquino, 41 said, “so you cultivate and eat whatever grows.”

What grows is mainly yuca or cassava and corn, which is sacred to the native Guaraní people. But what local dishes lack in pizazz, she said, they make up for in flavor and meaning.

Paraguayans still knead yuca starch and milled corn to make chipa during Holy Week. They infuse their yerba mate with fragrant herbs like boldo, burro, and begonias. They stuff their soups, stews and casseroles with aniseed, saffron, cloves, nutmeg, paprika and cilantro, all purveyed by Mickey in serving-size sachets.

“A moment, a taste, an aroma is a memory,’’ said Ms. Aquino, as a sopa paraguaya — a spongy “soup” made with Mickey corn flour — turned golden-brown in her oven. “And that memory can generate so many emotions. It’s your mom’s or your grandmother’s cooking.’’

Mickey’s popularity, she said, also has a lot to do with the mascot handing out candy outside the factory gates every Christmas: a tradition dating back to 1983.

Ms Aquino recalled feeling goose bumps as she waited outside the factory during the annual festivity in the early 1990s.

“There was no social media, there were no cellphones, there was nothing,” Ms. Aquino said. “Then suddenly Mickey comes along, and you’re like, ‘Wow!’ It was madness.”

“He’s a rock star,” she said.

By now, a “peaceful coexistence” reigns between Mickey and its United States doppelgänger, said Elba Rosa Britez, 72, the smaller company’s lawyer.

This truce was hard-won.

In 1991, Disney filed a trademark violation claim with Paraguay’s Ministry of Business and Industry that was rejected. The company then filed a lawsuit, but in 1995 a trademark tribunal ruled in Mickey’s favor.

Disney appealed again, taking the dispute to Paraguay’s highest court.

There, one judge agreed that Paraguayans could easily confuse the Disney Mickey and the Paraguayan Mickey.

But Disney didn’t reckon on a “legal loophole,” Ms Britez explained.

The Mickey trademark had been registered in Paraguay since at least 1956 — and Pascual’s descendants had since renewed it — without protest from the multinational.

In 1998, Paraguay’s Supreme Court issued its final ruling. Through decades of uninterrupted use, Mickey had acquired the right to be Mickey.

“I jumped for joy,” Ms Britez said.

Mickey’s legal immunity in Paraguay, Ms. Blasco acknowledged, might not extend to selling its products abroad. “We’ve never tried.”

The Paraguayan firm that represented Disney declined to comment. Disney officials did not respond to requests for comment.

During a recent national holiday, the man inside the Mickey mascot costume was warming up in an air-conditioned metal container inside the company’s factory that serves as his office.

Ms. Blasco asked The New York Times to withhold Mickey’s identity from the Paraguayan public to preserve some of the “magic” behind the mascot.

“Seeing the smiles on the kids’ faces is priceless,” the mascot said, before straightening his bow-tie and strolling out to his adoring public.

“Mickey!” they shouted, “Mickey!”

Mickey posed for photos, scattered sweets into strollers and passed popcorn through car windows to wide-eyed toddlers. Bus drivers honked their horns. A road-building crew waved. A worker leaned out of a garbage truck, pumped his fist and yelled: “Hey, Mickey!”

Some lining up to meet the mascot said Mickey’s David-vs-Goliath triumph against Disney filled them with national pride.

“It’s nice,” laughed Maria del Mar Caceres, 25, a stay-at-home mother. “At least we won at something.”

President Biden’s deliberations with Prime Minister Keir Starmer of Britain about whether to allow Ukraine to attack Russia with long-range Western weapons were fresh evidence that the president remains deeply fearful of setting off a dangerous, wider conflict.

But the decision now facing Mr. Biden after Friday’s closed-door meeting at the White House — whether to sign off on the use of long-range missiles made by Britain and France — could be far more consequential than previous concessions by the president that delivered largely defensive weapons to Ukraine during the past two and a half years.

In remarks at the start of his meeting with Mr. Starmer, the president underscored his support for helping Ukraine defend itself but did not say whether he was willing to do more to allow for long-range strikes deep into Russia.

“We’re going to discuss that now,” the president told reporters.

For his part, the prime minister noted that “the next few weeks and months could be crucial — very, very important that we support Ukraine in this vital war of freedom.”

European officials said earlier in the week that Mr. Biden appeared ready to approve the use of British and French long-range missiles, a move that Mr. Starmer and officials in France have said they want to provide a united front in the conflict with Russia. But Mr. Biden has hesitated to allow Ukraine to use arms provided by the United States in the same way over fears that President Vladimir V. Putin of Russia would see it as a major escalation.

On Thursday, Mr. Putin responded to reports that America and its allies were considering such a move by declaring that it would “mean that NATO countries — the United States and European countries — are at war with Russia,” according to a report by the Kremlin.

Mr. Biden and Mr. Starmer offered little insight on Friday into the actions they planned to take. But officials on both sides of the Atlantic said they did not expect any announcement immediately after the White House meeting. In the past, Western countries have begun providing new military equipment to Ukraine without announcing the decision publicly.

“This wasn’t about a particular decision that we’ll obviously pick up again in UNGA in just a few days’ time with a wider group of individuals,” Mr. Starmer told reporters after the meeting, referring to the annual meeting in New York of the United Nations General Assembly at the end of the month.

But he also hinted that he expected a decision about the missiles to come soon.

“I think if you look at both the Ukrainian situation and the Middle East, it is obvious that in the coming weeks and months there are really important potential developments, whatever timetable is going on in other countries,” he said.

John F. Kirby, the national security spokesman at the White House, said Friday that the Biden administration takes Mr. Putin’s threats seriously because he has proved himself capable of “aggression” and “escalation.” But Mr. Kirby added that there had been no change in Mr. Biden’s opposition to letting Ukraine use U.S. missiles to strike deep inside Russia.

“There is no change to our view on the provision of long-range strike capabilities for Ukraine to use inside Russia, and I wouldn’t expect any sort of major announcement in that regard coming out of the discussions, certainly not from our side,” he said.

Mr. Kirby’s comments came just hours before the two leaders met for their first lengthy conversation since Mr. Starmer became prime minister in early July.

The question of whether to let Ukraine use the long-range weapons that can travel 150 to 200 miles has been a rare point of disagreement between British and American officials, who have largely been in lock step on strategy over the past 30 months of fighting.

British officials have argued that Ukraine cannot be expected to fight effectively unless it can attack the military sites that Russia is using to shoot missiles or the airplanes that deliver “glide bombs.” And they believe that Mr. Putin, for all his nuclear threats warning that war between Russia and European forces could be coming, is largely bluffing. Mr. Putin, they say, has shown he does not want to bring NATO directly into the fighting.

Mr. Biden’s view has been far more cautious.

He has hesitated at every major decision point, starting with shipping HIMARS artillery, then through debates on whether to send M1 Abrams tanks, F-16 fighters, and short- and long-range ATACMS, a missile system critical to American preparations to defend both Europe and the Korean Peninsula.

But those decisions have primarily helped Ukraine’s military defend its territory and try to repel the Russian invasion. Over time, his aides say, they have discovered that Mr. Putin was less sensitive to the introduction of new weapons into the battlefield than they had thought. So they have gradually approved more capable, longer-range arms for Ukraine.

The questions of how Mr. Putin would react to the use of American weapons by Ukraine to strike deep inside Russian territory, officials say, could lead to a very different outcome.

“When he starts brandishing the nuclear sword, for instance, yeah, we take that seriously, and we constantly monitor that kind of activity,” Mr. Kirby said. “We have our own calculus for what we decide to provide to Ukraine and what not.”

The American concerns are twofold. The first has been rooted in Mr. Biden’s concern that the war not escalate; time and again he has told members of his staff that their No. 1 priority was to “avoid World War III.”

The second American concern is a practical one: Pentagon officials do not believe Ukraine has enough of the ATACMS, the British Storm Shadow and the French SCALP missiles to make a strategic difference on the battlefield. The reach of the missiles, they note, is well known — and Russia has already moved its most valuable aircraft beyond the range the missiles can fly.

Moreover, the U.S. officials say, they simply cannot supply many more to Ukraine. The Pentagon has warned that it must keep a healthy reserve of weapons in case of an outbreak of fighting in either Europe or Asia. And the missiles are so expensive that they contend Ukraine could get more firepower putting that money into drones.

So in the American telling of events, the decisions being debated by Mr. Biden and Mr. Starmer are more symbolic than substantive.

Looming over this is the American election.

In the debate against Vice President Kamala Harris on Tuesday, former President Donald J. Trump declined several opportunities to say he was committed to Ukraine’s victory. Instead, he talked of striking a deal, one that Ukraine may be coerced to sign.

While Ms. Harris is likely to continue the outlines of the American strategy, providing more arms and aid to Ukraine as long as Congress keeps the spigot open, Mr. Trump has made clear he is uninterested in continuing to spend heavily. And while Europe has stepped up, it does not have enough of an arsenal to make much of a difference.

Early this summer, Amin Abed, a Palestinian activist who has spoken out publicly about Hamas, twice found bullets on his doorstep in northern Gaza.

Then in July, he said he was attacked by Hamas security operatives, who covered his head and dragged him away before repeatedly striking him with hammers and metal bars.

“At any moment, I can be killed by the Israeli occupation, but I can face the same fate at the hands of those who’ve been ruling us for 17 years,” he said in a phone interview from his hospital bed, referring to Hamas. “They almost killed me, those killers and criminals.”

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