Tensions were high on both sides of the Israeli-Lebanese border on Monday as Israeli leaders vowed to deliver a significant military blow against the armed group Hezbollah in response to a deadly rocket attack over the weekend.

The attack on Saturday killed 12 children and teenagers in the Druse Arab village of Majdal Shams in the Israeli-controlled Golan Heights.

Hezbollah, an Iran-backed militia that dominates southern Lebanon and that has been firing rockets into Israel for months, denied responsibility for the strike. But Israel and the United States blamed the group, saying it was Hezbollah’s rocket that had been fired from territory it controls.

Israel’s prime minister, Benjamin Netanyahu, who visited the site of the attack on Monday, said, “Our response is coming, and it will be severe.” Local residents heckled Mr. Netanyahu, telling him they had no security and chanting, “Murderer! Murderer!” videos posted on social media showed.

Mr. Netanyahu’s visit to Majdal Shams came the morning after Israeli cabinet ministers authorized him and Israel’s defense minister, Yoav Gallant, to determine the nature and timing of the military response. The strike and Israel’s expected counterattack have raised fears that nearly 10 months of armed conflict between Israel and Hezbollah could spiral into an all-out war.

Hezbollah began firing rockets, antitank missiles and drones into Israel in solidarity with Hamas after that group, which is also backed by Iran, led the deadly Oct. 7 attack on southern Israel.

Israel and Hezbollah have since fired thousands of missiles across the border, wrecking towns, killing hundreds, displacing tens of thousands on both sides of the lines and leading each to threaten the other with a ground invasion. The strike on Majdal Shams was the deadliest attack on civilians in Israeli-controlled territory since the Hamas assault in October.

Israeli analysts said Hezbollah was most likely aiming at a nearby army base on Mount Hermon and did not intentionally target the village. But the group’s use of inaccurate rockets led to the kind of civilian bloodshed that could ignite a full-blown war, they said, even as Israel continues to wage a devastating military offensive against Hamas in the Gaza Strip.

Since the rocket strike on Majdal Shams, Western diplomats have been scrambling to try to defuse tensions between Israel and Hezbollah.

On Monday, Secretary of State Antony J. Blinken, speaking by phone with President Isaac Herzog of Israel, reaffirmed the United States’ “ironclad commitment” to Israel’s security, according to a State Department spokesman, Matthew Miller.

But Mr. Blinken also emphasized “the importance of preventing escalation of the conflict and discussed efforts to reach a diplomatic solution” with Hezbollah, Mr. Miller said.

John F. Kirby, a spokesman for the U.S. National Security Council, expressed confidence on Monday that a wider war between Israel and Hezbollah could be avoided.

“Israel has a right to defend itself — no nation should have to live with this kind of threat,” he told reporters in Washington. At the same time, Mr. Kirby said, “we believe that there is still time and space for a diplomatic solution.” He added, “Nobody wants a broader war, and I’m confident we’ll be able to avoid such an outcome.”

Ehud Yaari, an Israel-based fellow of the Washington Institute for Near East Policy, said Israel needed to respond to meet the expectations of the minority Druse community and Israeli public opinion in general to not show weakness to the enemy.

The Israeli response would most likely be carefully focused in the hope of preventing a prolonged escalation, Mr. Yaari added. Options for a response could include targeting more senior Hezbollah figures or some of the group’s more valuable military assets.

One problem, he said, was that Hezbollah had already gone into “emergency mode” and had evacuated facilities that it considered vulnerable in Lebanon and Syria.

There have been continued attacks across the border since the strike on Majdal Shams, but they seem to have fallen within the limits of the tit-for-tat strikes of the past few months. The Israeli military said overnight that its aerial defense systems had intercepted a pilotless aircraft that crossed from Lebanon into northwestern Israel.

On Monday morning, a drone strike on a vehicle in southern Lebanon killed two people and injured three others, including a child, according to Lebanon’s state-run news agency. At least two Lebanese towns were also hit overnight by Israeli airstrikes, the agency reported.

The Israeli military said in a statement that approximately 20 projectiles had crossed from Lebanon on Monday morning and had fallen in an open area in northern Israel, causing no injuries. Within minutes of those launches, the military said, its air force had struck the launcher in southern Lebanon.

Israeli aircraft also hit additional Hezbollah targets during the day, the statement added, eliminating what the military described as a Hezbollah cell.

Many in Lebanon were relieved on Monday that there had been no major Israeli retaliation overnight. Children made their way to school. Bakeries fired up their ovens, and roads were clogged with traffic as people went about their daily commutes.

“It was cool to wake up and find that I was alive,” said Mohamed Awada, 52, a taxi driver and father of two who lives in the southern suburbs of Lebanon’s capital, Beirut. The area is controlled by Hezbollah, and many Lebanese fear it could be targeted in any Israeli response.

Embassies in Lebanon reissued warnings against travel to the country and urged foreign citizens to leave while flights were still available.

Rena Bitter, the American assistant secretary of state for the bureau of consular affairs, described a “complex and quickly changing situation” in a video released by the American Embassy in Beirut on Monday.

Ms. Bitter said that Americans in Lebanon “should be prepared to shelter in place for long periods” if commercial flights were halted. “We recommend that U.S. citizens develop a crisis plan of action and leave before a crisis begins,” she said.

Some airlines, including the Lufthansa Group, suspended or adjusted their flight schedules in Lebanon amid the heightened tensions. Middle East Airlines, Lebanon’s national carrier, cited “insurance risks” as a reason for rescheduling overnight flights arriving in Beirut, according to a statement.

Adding to tensions in the region, President Recep Tayyip Erdogan of Turkey on Sunday raised the possibility that his country’s forces could enter Israel in response to the Israeli invasion of Gaza.

“We should be very strong so that Israel cannot do this stuff to Palestine,” Mr. Erdogan said while addressing members of his governing Justice and Development Party in the Black Sea city of Rize, his ancestral hometown.

“Just like we entered Karabakh, just like we entered Libya, we can do similar to them,” he added, referring to Turkish support for Azerbaijan in its conflict with Armenia last year and his country’s military intervention in Libya. “There is no reason not to do it,” he continued. “We must be strong to take these steps.”

It was unclear whether his comments were intended to appeal to his political base.

Throughout the war in Gaza, Mr. Erdogan has expressed support for Hamas, referring to it as “an organization of liberation” while harshly criticizing Israel. He has compared Mr. Netanyahu to Hitler and has called him a “psychopath” and a “vampire.”

Israel’s foreign minister, Israel Katz, said on Sunday that Mr. Erdogan was following in the footsteps of Saddam Hussein, the Iraqi ruler who was executed in 2006.

Diplomatic relations between Turkey and Israel broke down in the early months of the war, and in May, Turkey announced that it was halting trade with Israel.

Reporting was contributed by Hwaida Saad, Edward Wong, Gabby Sobelman, Ben Hubbard, Safak Timur, Myra Noveck, Patrick Kingsley, Peter Baker and Michael Levenson.

Bags of sugar that leave the Dalmia Bharat Sugar mill in the western Indian city of Kolhapur come with an industry guarantee: It was harvested humanely, in fields free of child labor, debt bondage and abuse.

None of that is true.

The mill is certified by a group called Bonsucro, which sets the industry standard for sugar production. Brands including Coca-Cola, PepsiCo, Unilever and General Mills use the Bonsucro name to reassure customers that their supply chains demonstrate “respect for human rights,” even in places where abuses are widespread, like the region around the Dalmia mill.

But a New York Times investigation found that Bonsucro’s inspections were all but guaranteed not to find problems. Internal documents and interviews with sugar mill executives, experts and Bonsucro contractors show that mills retain tremendous control over what auditors see and whom they can talk to. The audits are carried out hurriedly — from the mill to the farms in a matter of days — and the details are kept secret, which prevents public second-guessing.

Even the auditor who said she inspected the Dalmia mill said turning up problems was extremely rare.

“I’ve been auditing for the last two years, and I have not found any violations,” said Swapnali Hirve, a contract Bonsucro auditor who said she also inspected a mill owned by NSL Sugars. Both mills are in the state of Maharashtra.

But women who cut sugar cane that ends up in these mills work in brutal conditions. In interviews, they told us that they were pushed into underage marriages so that they could cut sugar with their husbands. They were locked into years of debt by sugar mill contractors. Some, like thousands of other working-age women in this region, said they felt pressured to get unneeded hysterectomies to resolve common ailments like painful periods and keep working in the fields.

One woman we talked to said that a contractor for the NSL mill even lent her the money for the surgery.

Yet Bonsucro certified the Dalmia mill. Two framed certificates, bearing Bonsucro’s olive green logo, hung in the factory’s back room during a visit last fall. NSL’s mill also passed its inspections and is in the process of being certified, mill executives said last year.

The audits are particularly notable because Bonsucro was warned years ago about debt bondage and child labor in India, records show. And Bonsucro’s chief executive, Danielle Morley, said in an interview that she knew about the unusually high rate of hysterectomies among sugar cane cutters in Maharashtra — even before a Times investigation in March.

Ms. Morley said that inspectors were never specifically told to look for evidence of coerced hysterectomies but will be from now on. “Going forward,” she said, “that’s what we’ve committed to.”

But she said the problem had deep social and economic roots that Bonsucro alone could not solve.

Bonsucro engages in what is known as social auditing, an inspection process that certifies many products that people consume or wear — especially those with labels like “sustainably produced.” Sometimes companies do the auditing themselves. Often, they outsource it to one of a niche industry of firms.

Human rights groups have argued for years that social auditing paints over abuses. And scholars have questioned whether groups like Bonsucro improve labor conditions.

“The question you need to ask is, what is the ultimate purpose of these organizations?” said Philip Schleifer, a professor at the University of Amsterdam who has researched Bonsucro. “Is it really to address problems, or to serve powerful companies?”

In Maharashtra, human rights problems persist in part because practically everybody says they are someone else’s responsibility. Factory owners blame the middlemen contractors who hire the laborers. Dalmia and NSL executives, for example, say that they do not directly employ the laborers, do not dictate the working conditions in the fields and see hysterectomies as a wider issue unrelated to the industry.

Contractors, in turn, say the factories are responsible. Big sugar-buying companies — both Indian and international — say it is tough to monitor farms. And consumers often have no idea about the origins of the sugar in the products they buy.

Bonsucro was meant to help fix that. Instead, its inspections have sent a false message that sugar mills that profit off abusive labor are actually problem-free.

In Maharashtra, hysterectomies are an extreme yet common consequence of this abusive system. Sleeping on the ground, giving birth in the fields and forgoing doctor visits can cause a host of gynecological problems. Faced with the misery of menstruating in 100-degree heat without running water or shelter, many women have hysterectomies to end their periods or to treat routine health conditions. Removing a uterus and ovaries can have lasting health consequences, especially for a working-age woman.

“My working conditions in the sugar cane fields led me to have a hysterectomy,” said Anita Bhaisahab Waghmare, a sugar cane cutter in her 40s who said she had worked since she was 13 for a contractor for the Bonsucro-certified Dalmia mill.

Auditors, though, say they have too few chances to speak to workers like Ms. Waghmare. The inspection process is highly stage-managed. Factory executives say they tell inspectors which farms they can visit — and choose only the best.

Bonsucro employs 30 people, many of whom operate from a London co-working space. The organization hires contractors to conduct the inspections, which are typically paid for by the factories themselves.

“We’re trying to do the right thing in a difficult sector with relatively limited resources,” Ms. Morley said.

Bonsucro said that Dalmia was vetted under an old standard. Only some fields were audited and, while the factory itself was certified, only some of its sugar qualifies. When the factory is recertified, Bonsucro will look at its supply chain more broadly.

Even after a Times investigation linked both Dalmia and NSL to labor abuses, Bonsucro did not sever ties with either company. Ms. Morley said Bonsucro was in discussions with the companies about the reported abuse.

But in the supply chains of the two mills that Bonsucro inspected, she said, her auditors saw no evidence of it.

How Did This Happen?

Bonsucro was formed in the mid-2000s at a critical moment.

Brands like Nike had faced boycotts over child sweatshop labor. Oil companies were under fire for pollution. Western companies faced the possibility of government regulation at home over labor and environmental practices abroad.

Sugar had not come under particular scrutiny, but it was widely known as one of the world’s most exploitative industries, involving a water-guzzling crop that requires backbreaking labor to harvest. Sugar cane farming conjured images of the cruelty of the trans-Atlantic slave trade.

Other industries had developed an answer to this threat of regulation. They embraced social auditing and formed certification bodies to inspect supply chains and hold companies to a standard.

For companies, it was a win-win. It allowed them, not governments, to set standards. And it signaled to the public that they worked with clean factories and humane suppliers.

While most advocacy groups preferred government regulation, a few embraced this model. Passing laws is hard. Better, they figured, to get companies to change on their own.

That is how Bonsucro began, as a mix of nonprofit groups and big sugar buyers: the World Wildlife Fund, Coca-Cola, Cargill and others.

WWF got involved as part of its broader ecological mission because sugar consumes so much water. Its participation was novel for an environmental group, Professor Schleifer said. “Earlier, there was a focus on more confrontational tactics, like boycotts,” he said.

In a 2004 internal memo that we reviewed, Jason Clay, of WWF said that a certification program would provide needed oversight. “My assessment was, we would never get governments to set regulations,” Mr. Clay said in an interview. “But we could get companies to.”

The case for social auditing assumes that consumers will pay a premium for green, humanely made products. Customers seem willing, for instance, to pay a little more for products like coffee that are stamped with the Fairtrade logo.

Sugar is different. Sugar from a variety of sources gets mixed together before it arrives on grocery store shelves. And consumers do not necessarily drive sales of sugar. Big companies like Tate & Lyle, Coca-Cola and Unilever do.

And according to sugar mill owners and others involved with Bonsucro, big companies were rarely willing to pay a premium for certified sugar.

That conflict lies at the heart of Bonsucro. Its seal of approval carries little value with customers. So sugar mills have little financial incentive to improve their practices to seek certification.

“It sounds like a minor difference,” one former Bonsucro member said. “But it’s huge.”

‘This Isn’t the Real Scenario’

Bonsucro focused first on Latin America, where a few dominant players often control much of the sugar cane harvest. That made audits relatively straightforward.

India, the world’s second-largest sugar producer, was more complicated. Each mill buys from thousands of farms, all of which would need to be audited to truly certify a supply chain.

“Organizing the smallholder farmer world in relation to migrant workers is beyond what Bonsucro can solve,” said Jeroen Douglas, a sustainability activist who was involved in the discussions around Bonsucro’s founding.

When auditors arrive in Maharashtra, they face a daunting question: Which farms should they inspect?

NSL Sugars, for example, buys from thousands of farms, said A. Arulappan, a company executive. When Ms. Hirve, the auditor, arrived, the company provided her with a list to choose from.

“We select good, progressive farmers, with loyalty to our unit,” Mr. Arulappan said in an interview.

Ms. Hirve, who conducted Bonsucro audits on behalf of the firm Control Union, acknowledged starting with what the mills give her. “They submit a farmer list,” she said. “During the audit, we choose the sample randomly.”

Ms. Morley, the Bonsucro chief executive, said she was surprised to hear that mill executives handpicked the farms. She called it “problematic.”

Sugar mill officials then accompany auditors to farms, Mr. Arulappan said. But auditors rarely speak to sugar cane cutting laborers, a Dalmia executive, S. Rangaprasad, said.

That oversight gap is significant because records show that Bonsucro was warned years ago that its inspections were insufficient at spotting abuses that were known to be rampant in India.

In 2018, Bonsucro commissioned a team of Columbia University graduate students to evaluate its effectiveness. The students focused on India. Before they left, they read local news and researched the Maharashtra sugar industry. They knew they were heading into a system that could be deeply harmful to workers.

When they arrived, though, they encountered many of the same obstacles that supply chain auditors face while inspecting sugar mills.

Sugar mill owners gave the Columbia team lengthy interviews but tightly restricted their access to the fields and workers.

“They planned it very strategically to make sure we did not reach the farmers directly,” said Priya Patil, an auditor who worked as an interpreter for the project. “There were moments where I felt like, ‘This isn’t the real scenario.’”

In 2019, a local government report revealed what those conversations might have yielded. Researchers surveyed 82,000 female sugar cane workers and documented abuses including debt bondage and child labor. About one in five women had undergone hysterectomies.

The Columbia team released its report that same year. It noted a series of risks — child labor, debt bondage and gender discrimination — but said that the researchers had been so tightly controlled that they could not study them.

In some cases, the researchers wrote, Bonsucro’s oversight system was unlikely to catch these abuses either. Because none of the audit details are public, nobody could know for sure. “These concerns underscore the weaknesses of social auditing,” they wrote.

Bonsucro does not make audit details public, Ms. Morley said, because companies would have to agree to it. “Everything that we do has to be discussed and negotiated and agreed upon by all of our members.”

She concedes that social auditing is flawed and can miss serious problems. “The challenges are quite well documented,” she said. But she said that Bonsucro was helping to change the industry by pushing for companies to improve their practices.

“The sugar cane sector is going on a journey of improvement,” she said. “But it does come from a fairly low base line.”

Qadri Inzamam, a reporter with The Fuller Project, contributed reporting from Beed, India. Alexandra Regida contributed research.

When Iraq’s prime minister traveled to Washington in the spring, he hoped to negotiate a much-needed economic development package and discuss shared strategic interests with the United States, one of his country’s most important international allies.

But the very day he arrived in mid-April, events unfolding at home served as a stark reminder of the competing influences that the Iraqi prime minister, Mohammed Shia al-Sudani, is caught between: Iran was sending drones and missiles to attack Israel and at least one Iraqi militia backed by Tehran participated in the attack.

Both the United States and Iran have long held sway in Iraq. But since the war between the U.S. ally Israel and the Iran-backed Hamas broke out in Gaza almost 10 months ago, they are increasingly at odds.

With regards to Iraq, one of the most contentious issues is the continued presence of 2,500 American troops on Iraqi soil. Over the past 20 months, Iran has used its considerable influence to try to persuade the Iraqis to push those forces out, and if it succeeds, it would give Tehran even more say over Iraqi policies.

Last week, in the latest round of discussions in Washington on a reconfiguration of the military relationship, Iraq called for a drawdown of the U.S.-led multinational force within about a year, underscoring its determination to thin out the American presence.

Iran’s clout in Iraq has grown in the past few years as Iraqi Shiite political factions close to Tehran have come to dominate the national government. At the same time, the Iraqi militias that Iran has cultivated over the past 20 years have come to form a growing part of the national security forces since they were folded in a few years ago.

The militias form part of Iran’s network of proxy forces in the Middle East, including Hezbollah in Lebanon and Hamas in Gaza. The war in Gaza has escalated tensions regionally, and the American, British and Israeli governments have all noted that Iraqi proxies of Iran joined in the April attack on Israel — in defiance of demands by Prime Minister al-Sudani to stay out of the conflict.

Most recently, a rocket from Lebanon on Saturday killed at least 12 children and teenagers in an Israeli-controlled town in the Golan Heights. The United States and Israel blamed Hezbollah, but the group denied responsibility.

Even before the Iraqi militias participated in the attack on Israel, a senior member of Iraq’s security forces, Abdul Aziz al-Mohammedawi, made no attempt to hide his allegiance to Tehran.

Israeli warplanes hit an Iranian diplomatic compound in Syria in April, preceding the Iranian attack on Israel. After the Israeli strike, Mr. al-Mohammedawi said the forces he oversees were awaiting orders from Ayatollah Ali Khamenei, Iran’s supreme leader, while making no mention of Iraq’s prime minister.

Mr. al-Mohammedawi is the chief of staff of Iraq’s Popular Mobilization Forces, an umbrella organization for militias that now encompasses more than 170,000 fighters, including a number of brigades backed by Iran. His announcement suggested that at least some Iraqi forces were ready to attack Israel on Iran’s behalf — a startling proclamation from such a senior Iraqi security official.

Publicly, the Iraqi prime minister said nothing, perhaps suggesting his reluctance to openly confront those closest to Iran.

Iran’s goal is clear, said Sajad Jiyad, an Iraqi analyst and fellow at Century International, a research and policy nonprofit in New York.

“The Iranians always say: ‘This is our region. America doesn’t live here. America is on the other side of the world. What’s it doing here?’”

Still, Iraq is the last Middle Eastern country where there has been something of a balance between Iranian and U.S. interests for many years now. At times, those interests have even converged, for example when both powers supported Iraq’s military offensive to expel the Islamic State terror group.

As prime minister, Mr. al-Sudani has often managed to finesse competing U.S. and Iranian demands. But whether to allow American troops to remain on Iraqi soil is one of the thorniest dilemmas he faces.

In addition to some 2,500 American forces in Iraq, 900 more, most of them Special Operations forces fighting in Syria, are supported by the U.S. contingent in Iraq and pass through Iraq regularly for resupply and training. Those in Syria are fighting alongside Syrian Kurdish forces in an attempt to keep remnants of the Islamic State in check.

U.S. forces have been on the ground in Iraq off and on since the 2003 invasion that ousted the longtime dictator Saddam Hussein. They withdrew completely in 2011. But after the Islamic State invaded Iraq in 2014 and took control of much of the country’s north, the Iraqi government asked the U.S. military to return.

A U.S. troop withdrawal would amplify Iran’s influence over Iraqi foreign policy — much in the way that Tehran influences Lebanon, Syria and Yemen, the other Middle Eastern countries where it has cultivated powerful proxy forces — according to Urban Coningham, a Middle East research fellow at the Royal United Services Institute in London.

In some of these cases, the armed groups that Iran fostered in those countries are now so strong they effectively control the governments, making them important vessels for Iran to project its anti-Western agenda across the Middle East.

But Iraq is different.

For one, the United States has had a far greater stake in the country and still wields considerable leverage there, in part because many Iraqis — inside and outside the government — have welcomed it as a counterweight to Iran. But since Iraqi Shiite parties close to Iran gained the greatest share of power after the 2021 parliamentary elections, demands for a speedy drawdown of American forces have moved front and center.

The prime minister and his advisers have tried to take a nuanced position. They are hoping for a reconfiguration that guarantees some continued U.S. military involvement, supplies of much-needed equipment and ongoing training. It would entail some troop withdrawals, which they could present as a drawdown to satisfy the demands of the pro-Iran political factions.

However, Iran is pressing hard for all American troops to leave as soon as possible. Iraqi political leaders close to Iran are backing that position.

Mahmoud Al-Rubaie, a longtime strategist for Asa’ib Ahl al-Haq, one of the most influential of the Iraqi political parties close to Iran, said the U.S. image in Iraq had worsened since the 2003 American-led invasion of the country.

“The generation of 2003 had hopes and dreams that the U.S. would change the reality of the country,” he said. But as the U.S. troop presence stretched out over the years, the Iraqi people did not see the transformation they had hoped for, he added.

Those views hardened — especially among the country’s Shiite Muslim majority — in 2020 after the U.S. assassination of a top Iranian general, Qassim Suleimani, in Baghdad, said Mr. Al-Rubaie.

General Suleimani headed the Quds Force, the overseas arms of the powerful Iranian Revolutionary Guards. He was the architect of Iran’s regional network of proxy forces, including some of the Shiite militias in Iraq, which he helped to recruit, train and initially finance.

Mr. Jiyad of Century International said one of Iraq’s major weaknesses “is that we do not have a cohesive government or cohesive policies and so that makes our country reactive to outside influence.”

Falih Hassan contributed reporting from Baghdad.

A third child has died after a knife attack in Southport, England, and five children and two adults remain in a critical condition, the police said on Tuesday.

A 9-year-old girl died in the hospital in the early hours of Tuesday, the police said in a statement, while two other girls, age 6 and 7, died on Monday as a result of their injuries.

The attack, which the local police chief, Serena Kennedy, described as “ferocious,” took place at a Taylor Swift-themed dance class for children age 6 to 11. A 17-year-old boy was arrested and is being questioned by the police.

Ms. Swift said in a statement about the attack on Instagram that she was “completely in shock.”

“The horror of yesterday’s attack in Southport is washing over me continuously,” she wrote, adding: “The loss of life and innocence, and the horrendous trauma inflicted on everyone who was there, the families, and first responders. These were just little kids at a dance class.”

Prime Minister Keir Starmer is expected to visit the scene on Tuesday, Rachel Reeves, the chancellor of the Exchequer, told Sky News.

Here’s what we know.

How did the attack unfold?

A group of children were attending a Taylor Swift-themed yoga and dance workshop at a studio in Southport on Monday when the attack took place.

The suspect arrived in a taxi and refused to pay for the trip, according to witnesses. A local businessman, Colin Parry, told the Guardian newspaper that a member of his staff had seen several children running out not long after, all bleeding.

Police officers who arrived at the scene just before noon “were shocked to find that multiple people, many of whom were children, had been subjected to a ferocious attack and had suffered serious injuries,” Ms. Kennedy, the chief constable of the Merseyside Police, said in a press briefing on Monday night.

She added that all those injured had suffered stab wounds during the incident.

What do we know about the victims?

The event, a yoga, dance and bracelet-making workshop, was advertised on social media for children age 6 to 11. Many schools in Britain started their summer vacation last week, and the event was sold out. “Calling all Swifties!” read a post on Instagram, next to a digital flier with a pink and purple background.

Three girls have died as a result of the attack, while eight other children were injured, five of them critically, the police said.

The police identified the girls who were killed as Bebe King, who was 6; Elsie Dot Stancombe, 7; and 9-year-old Alice Dasilva Aguiar.

In a statement, the King family said, “No words can describe the devastation that has hit our family.”

The Dasilva Aguiar family were also quoted in the statement. “Keep smiling and dancing like you love to do, our princess,” they said in a tribute.

Alice was also a Portuguese national, according to the Portuguese news agency Lusa. Her parents moved to England from the island of Madeira, and their daughter was born there, José Cesário, Portugal’s secretary of state told the agency.

Two adults were also injured at the scene and are in a critical condition.

“We believe that the adults who were injured were bravely trying to protect the children who were being attacked,” Ms. Kennedy, the chief constable, said.

Two Taylor Swift fans from Britain, Cristina Jones and Holly Goldring, started an online fund-raiser to assist the grieving families and injured children. Within hours, their JustGiving page had raised more than 100,000 pounds, about $128,000, from supporters around the world.

According to the organizers, the money will go to Alder Hey Children’s Charity, which raises funds for the children’s hospital in Liverpool where many of the victims were being treated.

“We have no intentions of reaching out to the families ourselves — it will be Alder Hey who will help” get money to families, Ms. Jones told the Press Association news agency. “We will keep a respectable distance,” she added.

What do we know about the suspect?

The police on Monday arrested a 17-year-old boy on suspicion of murder and attempted murder. The suspect lived in Banks, a nearby village, but is originally from Cardiff, Wales, the police said.

The suspect remains in custody and was being questioned on Tuesday. The police said they were still investigating the motive.

“At this moment in time, the investigation is not being treated as terrorist-related,” Ms. Kennedy said.

In the statement on Tuesday, the police also urged people not to speculate on the details of the attack while the investigation continued and said that a name circulated by some users on social media was “incorrect.”

Under British law, young people who are under criminal investigation cannot be named until they turn 18, except in very rare circumstances.

France has backed a plan for the autonomy of the long-disputed Western Sahara territory under Moroccan sovereignty, a diplomatic shift that immediately provoked condemnation from Algeria, a former French colony and Morocco’s rival in the region.

In a letter to King Mohammed VI of Morocco that was made public on Tuesday, President Emmanuel Macron of France said that Morocco’s plan was “the only basis for achieving a just, lasting and negotiated political solution in accordance with the resolutions of the United Nations Security Council.”

That was a notable departure from France’s prior position. The French authorities previously argued that Morocco’s plan for autonomy, which was put forward in 2007, was a “serious and credible” basis for discussion, but not the only one.

Excerpts from Mr. Macron’s letter, which were sent to the king on the 25th anniversary of his ascension of the throne, were made public on Tuesday by Mr. Macron’s office.

“I consider that the present and the future of Western Sahara fall within the framework of Moroccan sovereignty,” Mr. Macron wrote.

Western Sahara, once a Spanish colony, was annexed by Morocco in 1975, prompting a 16-year conflict with the Polisario Front, an independence movement representing the region’s Indigenous Sahrawi ethnic group. A United Nations-brokered cease-fire in 1991 was broken in late 2020, but the region has been stable recently.

Morocco welcomed France’s move, which came after similar shifts from other Western nations like Spain and the United States. In 2020, the Trump administration had recognized Moroccan sovereignty over the Western Sahara in exchange for normalizing relations with Israel.

France’s announcement is an “important and significant evolution in support of Moroccan sovereignty over the Sahara,” King Mohammed VI’s office said in a statement.

But the move was a blow to Polisario and to Algeria, which supports the Western Saharan separatist movement. Algerian authorities expressed “deep regret and disapproval” at the announcement, strongly denouncing it as “unexpected, ill-timed and counterproductive.”

“This French decision does not help to create the conditions for a peaceful settlement of the Western Sahara question, but rather reinforces the impasse created by Morocco’s so-called autonomy plan, which has lasted for more than 17 years,” the Algerian Ministry of Foreign Affairs said in a statement on Tuesday.

Sidi Omar, the Polisario’s representative at the United Nations, said on the social media platform X that “by taking a hostile and escalatory position toward the Sahrawi people, France has excluded herself from everything related to the international efforts to decolonise Western Sahara.”

France has over the past few years walked a tightrope in its diplomatic relations with Morocco, a former French protectorate, and Algeria, a former colony. The two North African countries have been bitter adversaries.

Relations between France and Morocco soured in recent years, after revelations that Morocco may have been monitoring Mr. Macron’s cellphone using the spyware Pegasus. France had also restricted delivering visas to Moroccan nationals despite years of historically strong ties between the two nations.

Mr. Macron has tried to reset relations with Algeria, which gained independence in 1962 after a brutal war and still has tense relations with France.

Mr. Macron, the first French president who was born after France left Algeria, has acknowledged the use of torture by French forces, and asked for forgiveness for the abandonment of the hundreds of thousands of Algerian Arabs, known as Harkis, who fought on the French side in the war of independence. His government established a commission to review the two countries’ colonial history.

But relations between France and Algeria have remained strained. France’s backing of Moroccan sovereignty over the Western Sahara seemed to acknowledge that the outreach toward Algeria had not been as effective as hoped.

In Morocco, the letter was met with celebratory headlines from the local news media. Adding to the positive news, the king on Monday pardoned hundreds of prisoners, including prominent journalists.

But it was unclear whether France’s move would have any immediate consequences on the Western Sahara dispute.

“I don’t see the new French position as a sea change in the evolution of the conflict,” said Aboubakr Jamai, a dean of the Madrid center at the Institute for American Universities.

“The United Nation process remains based on the principle of self-determination,” Mr. Jamai said. “It would have been a meaningful evolution if France championed a United Nations Security Council resolution rejecting the Sahrawi people’s right to self-determination.”

He added that “the Moroccan regime desperately needed a win on the Sahara issue.”

“Morocco sold the widely unpopular normalization with Israel as a quid pro quo for the recognition of its sovereignty on the Western Sahara,” he said. “The Gaza situation made Morocco’s position increasingly untenable vis-à-vis its public opinion.”

France’s move comes at a delicate political moment for Mr. Macron, whose government is currently acting only in a caretaker capacity after recent legislative elections yielded no clear majority.

Mr. Macron has refused to appoint a new government until after the Paris Summer Olympics. Political opponents have become increasingly critical of that stance, arguing that a caretaker cabinet, whose ministers have formally resigned, is in no position to make critical government decisions. France’s foreign policy is traditionally but not exclusively a presidential prerogative.

The authorities in Bangladesh have opened police cases against tens of thousands of people in recent weeks as security forces combed through neighborhoods as part of their deadly crackdown on a student protest that had spiraled into violence and carnage.

The widening legal net, confirmed in interviews with police officials and a review of records, comes as arrests surpassed 10,000 since the crackdown on protesters began two weeks ago. Charges range from vandalism and arson to theft, trespassing and damage of state property. In many of the cases, sections of the law that allows long-term detention were invoked.

“This is a witch hunt,” said Smriti Singh, the regional director for South Asia at Amnesty International.

The government of Prime Minister Sheikh Hasina has blamed opposition parties, mainly the Bangladesh Nationalist Party and Jamaat-e-Islami, for the deadly turn in a previously peaceful protest against a quota-based system for distributing sought-after government jobs. Conservative estimates put the death toll at more than 200, mostly students and youths.

Activists, analysts and diplomats say the movement escalated into chaos after the ruling party, having dismissed the students’ demands, unleashed its violent youth wing and a wide array of security forces.

The new detentions and the sweep for more arrests are meant to prevent any regrouping. Many of the student leaders have been detained, some repeatedly. But the crackdown also follows a well-established tactic under Ms. Hasina’s 15-year rule: using every opportunity to crush her political opponents by rounding up their leaders and dismantling their mobilization.

“We see ‘block raids,’ knocking on doors in the dead of night, asking if there are students inside. If there are, they check their phones. They do this on the streets, too,” Z.I. Khan Panna, a veteran supreme court lawyer and rights activist, told reporters on Monday. “In Bangladesh, in this age of information technology, anyone can check my phone, my diary, my pants. No one should have this right.”

Tallies by Bangladeshi newspapers have put the number of arrested at more than 10,000 and the number of accused of various crimes around the country at more than 200,000. More than 2,800 people had been arrested in the past two weeks in Dhaka alone as of Monday, police officials confirmed to The New York Times.

Many of the more than 240 cases filed in Dhaka also have a feature used often in Bangladesh in recent years: large numbers of unidentified people, accused en masse.

In Badda, a township in the north of Dhaka home to many universities, the police said they had filed 10 cases, with 8,000 to 10,000 people accused in each case. In the Mohammadpur area, the police had filed 12 cases, each with 3,000 to 4,000 people being accused. In Lalbagh, the number of accused was 9,000-10,000 and in Mirpur 8,000-9,000, according to police files.

The opening of such cases, coupled with flimsy evidence and an overzealous police force, are practices widely used in recent years by Ms. Hasina’s government, activists and analysts say. As she tried to cripple her opposition ahead of elections last year, in which she steamrolled to a fourth consecutive term, thousands were arrested in similar cases. The tactic was also used to quell protests seeking better pay from the garment industry, a key driver of the Bangladesh economy.

In many of the cases, the courts provide the accused some relief later, with the accusations falling apart because of a lack of evidence. But the accused still end up spending weeks, if not months, in jail, and long remain entangled in legal requirements and hearings that effectively sideline them from political work.

In recent days, as the communication blackout and curfew have been relaxed, Ms. Hasina’s administration has mixed optics of reconciliation with promises of punishment.

She announced Tuesday as a day of mourning, and met with families of victims of the protest violence. But the universities remain shut and the student leaders and political opponents are being detained around the country. The government has also announced that it would ban Jamaat-e-Islami, the country’s largest Islamist party.

“Instead of taking steps like ordering investigations into violations by the security forces to end the violence,” Ms. Singh said, “the Bangladesh government seems to be going to extreme extents to suppress dissent with a complete disregard to rule of law and due process.”