President Biden will be under increasing pressure this week to loosen restrictions on Ukraine’s use of weapons when global leaders converge on the United Nations for their annual gathering.

President Volodymyr Zelensky of Ukraine will also come with what he calls a victory plan for Mr. Biden to examine, and key European leaders are already pushing hard for Mr. Biden to allow him to use longer-range weapons supplied by NATO countries to hit farther inside Russia, to strike bases from which Russian planes and missiles attack Kyiv with relative impunity.

The push comes as Ukraine is slowly losing ground to mass Russian assaults in the eastern Donbas region and Russia continues to pound Ukraine’s civilian infrastructure, including electricity and heating plants, from a safe distance as winter is approaching.

Mr. Biden has been reluctant to give permission, careful as he has been since Russia invaded Ukraine in February 2022 not to escalate the war and risk a direct conflict between Moscow and the NATO alliance. President Vladimir V. Putin of Russia already blames NATO for the war and has made threats of retaliation, including frequent veiled references to his nuclear arsenal. But he has not retaliated militarily against the West even as NATO countries have gradually increased the quantity and quality of their arms supplies to Kyiv.

Finland’s new president, Alexander Stubb, joined the chorus for longer-range weapons in an interview with The New York Times, while Jens Stoltenberg, in his last days as NATO secretary general, has all but done the same, while noting diplomatically that each country must decide for itself.

Mr. Stubb, who will speak for all the Nordic countries at the U.N. General Assembly, was blunt.

“I call upon our allies in the global West, including the United States, to allow Ukraine to fight without one hand tied behind its back and to lift those restrictions,” he said in a wide-ranging interview on Thursday from Helsinki. “We need to continue to support Ukraine, starting with finance, starting with ammunition, starting with vehicles, and also with allowing Ukraine to use weapons as itself pleases, as long as it’s in self-defense and within the framework of international rules.”

Mr. Stoltenberg has been unusually outspoken as he prepares to leave office at the end of the month. “I fully understand the desire from Ukraine to have as few restrictions as possible,” he said in an interview with Christiane Amanpour of CNN. “There are less restrictions now than just some months ago,” he said, “and that’s the right thing to do,” because “this is a war of aggression” and “according to international law, self-defense is legal.”

Ukraine, he said, “has the right for self-defense and that includes striking legitimate military targets on the territory of the aggressor, Russia.” And NATO countries, he went on, “have the right to provide the weapons that they are using to do so without us becoming a party to the conflict.”

Both Mr. Stubb and Mr. Stoltenberg noted that various allied “red lines” had already been crossed, with the provision to Ukraine of Leopard II battle tanks, Storm Shadow and Scalp cruise missiles, longer-range artillery and even American-made F-16 fighter jets. All were subject to fierce debates over whether they would prompt Mr. Putin to escalate the fight and even use nuclear weapons.

The new prime minister of Britain, Keir Starmer, has also pushed Mr. Biden to allow the use of these longer-range weapons, like Storm Shadow and Scalp, its French version, to hit bases farther into Russia from where Mr. Putin launches attacks.

Adm. Rob Bauer, chairman of the NATO Military Committee, said last week that attacks deep inside Russia were legal, because “to weaken the enemy that attacks you, you not only fight the arrows that come your way but also attack the archer.” Still, he said, nations providing weapons can demand “certain limitations” in their use, “because they feel responsible for those weapons.”

Mr. Stubb, whose country joined NATO only in response to the war and shares a long border with Russia, has few illusions about what he considers NATO’s need to stand up to Russian aggression in Ukraine. “Russia is an imperial power that has expansion in its DNA,” he said.

“So what we need to do is to convince Putin that there’s no point for him to continue this war, and I think Putin needs to lose both the war and the peace, because the only thing that he understands is power,” Mr. Stubb said.

“The key is to allow Ukraine to fight this war without any kind of restrictions, and everything after that is secondary,” Mr. Stubb said. “The more we allow Ukraine to act, the sooner we will achieve peace negotiations.” Then the West must provide Kyiv with security guarantees leading to membership in both NATO and the European Union, he said.

Mr. Stoltenberg agreed. “By giving Ukraine more weapons, we can make Putin realize he cannot get what he wants by force and make it so costly that he will have to accept Ukraine has a sovereign, democratic right to persist as a sovereign, democratic country,” he said in a speech last week in Brussels to the German Marshall Fund. “The paradox is that the more weapons for Ukraine we are able to deliver, the more likely it is that we can reach a peace and end to the war. And the more credible our long-term military support, the sooner the war will end.”

Given raging global conflicts, including in the Middle East and Africa, the United Nations must re-engage in true peacekeeping, Mr. Stubb said. To that end, in New York, he said he would propose an expansion of the U.N. Security Council to include five new permanent members, one from Latin America, two from Asia and two from Africa, coupled with 10 rotating members and an elimination of the single-country veto, “which makes the Security Council dysfunctional,” he said. He would also propose that a member country “in blatant violation of the U.N. Charter and international law, such as Russia is right now in Ukraine,” should be suspended by a vote of the General Assembly.

Serious changes to the Security Council have proved impossible in the past, given the veto, he concedes, but he insists that the crisis demands new thinking. The veto might be replaced by weighted voting, he said, but it was crucial to include members of the so-called Global South, developing countries largely left out of post-1945 international institutions.

Those countries may see hypocrisy in the criticism of Russia and the support for Israel in Gaza, he said. “But my argument to our friends in the Global South, who are sometimes justifiably expressing doubts about Western double standards, is to say that this war in Ukraine sets the scene for how other nation-states can behave in the rest of the world,” he said. “If we now allow Russian imperialism to take place, we will see this happening elsewhere in the world, and that’s why I think this is a key struggle for all of us.”

When the United Nations General Assembly convenes on Tuesday, attention will focus on the major wars raging in Ukraine, Gaza and Sudan, amid a reckoning that neither the global body nor world powers have been able to end the violence.

By all accounts, the world has descended deeper into chaos and turmoil since last year’s annual gathering, when Russia’s invasion of Ukraine and Sudan’s civil war cast shadows. Now, those have been eclipsed by the Hamas-led Oct. 7 attack on Israel, and the war that followed in Gaza, with its catastrophic humanitarian toll on Palestinians.

The United Nations itself has had a turbulent year. A record number of its staff, 220 in total, have been killed in the war in Gaza. Its humanitarian resources, a crucial backbone of the global relief effort, are overstretched and underfunded as needs multiply rapidly because of wars, climate change and natural disasters. At the same time, its leadership struggles to play a meaningful role in conflict mediation.

“International challenges are moving faster than our ability to solve them,” said Secretary General António Guterres in a news conference this past week. “We see out-of-control geopolitical divisions and runaway conflicts — not least in Ukraine, Gaza, Sudan and beyond.”

The Security Council, which typically holds one session on the sidelines of the General Assembly, is scheduled to meet three times this year, on Ukraine, Gaza and the broader question of leadership challenges in resolving conflicts.

President Biden will address the General Assembly for the last time as his presidency draws to a close. With the exception of the European allies, the majority of U.N. member states have been highly critical of Mr. Biden’s staunch support of Israel and the United States’ blocking multiple calls for a cease-fire during the first eight months of the war.

Mr. Biden has in recent months led an effort, with Egypt and Qatar, to broker a cease-fire between Israel and Hamas and secure the release of all the hostages held by Hamas. But the talks have stalled, and the electronic devices attack in Lebanon this past week and an Israeli airstrike in Beirut on Friday that Lebanese officials said killed at least 45 people, seem to be dimming prospects of any breakthrough.

France’s president, Emmanuel Macron, and Prime Minister Keir Starmer of Britain will attend this year after both France and Britain sat out last year’s gathering. Ukraine’s president, Volodymyr Zelensky, will deliver three speeches in person, including at the Security Council meeting on Ukraine, where he is expected to present a new peace plan and renew his pleas to authorize Ukraine’s use of Western missiles to strike military targets deep inside Russia, diplomats said.

“It feels like we say this every year, but this year’s meeting could not come at a more critical and more challenging moment,” said Linda Thomas-Greenfield, the United States ambassador to the United Nations, at a briefing with reporters. “The list of crises and conflicts that demand attention and action only seems to grow and grow.”

Ms. Thomas-Greenfield said the United States would pursue three policy priorities during the General Assembly: international cooperation on peace and stability, improving global humanitarian aid responses, and revamping the Security Council.

Iran’s new reformist president, Masoud Pezeshkian, making his debut on the international stage, will be trying to present his government as moderate, pragmatic and open to diplomacy with the West, in contrast with his hard-line conservative predecessor, Ebrahim Raisi, who died in a helicopter crash in May.

That might not be an easy sell. Iran’s support of a network of militias in Lebanon, in Yemen and in Gaza and the West Bank, and recent reports that it is supplying Russia with ballistic missiles for its war against Ukraine, pose obstacles to defusing tensions with the West that Mr. Pezeshkian will struggle to overcome.

Richard Gowan, an expert on the United Nations with the International Crisis Group, said that the prospects for breakthroughs on Gaza or Ukraine at the assembly were bleak. But Sudan, Mr. Gowan said, could be an exception.

“I actually think the General Assembly could do some good on Sudan, probably in a way that it cannot on Gaza and Ukraine,” he said. “There is an emerging feeling among a lot of the U.N. membership that the U.N. failed unnecessarily on Sudan and that it’s time to push for more diplomacy.”

Climate change and rising sea levels will join with restructuring of the Security Council and the World Bank as major topics for discussion. For years, countries in Africa, Asia and South America have complained that the Security Council’s core group of five permanent, veto-wielding members — the United States, Britain, France Russia and China — is outdated, overlooking economic powers like India, Brazil and Japan, as well as the entire continent of Africa.

This month Ms. Thomas-Greenfield said that the United States supported adding two permanent African members to the Security Council and proposed starting preliminary negotiations on the matter. Washington also supports adding seats for Germany, India and Japan, but none of the new permanent members would have veto power.

Any changes to the Security Council require altering the U.N. charter and the approval of all current five members, a tall task given the divisions among Russia, China and the United States.

In an effort to spearhead the changes, Mr. Guterres will host a conference on Sunday and Monday, ahead of the General Assembly. The goal is for countries to approve three negotiated documents that are meant to serve as blueprints for addressing current and future challenges on climate, artificial intelligence, conflict and restructuring U.N. institutions.

“So many of the challenges that we face today were not on the radar 80 years ago when our multilateral institutions were born,” Mr. Guterres said. “Our founders understood that times would change.”

When Prime Minister Keir Starmer’s Labour Party won a whopping parliamentary majority in Britain’s election in July, it was with only 34 percent of the vote, leading one commentator to call it a “loveless landslide.” Now, some allies of Mr. Starmer worry that he is going too far in returning the favor.

The new prime minister has shown decidedly little love to a beleaguered British public, restricting payments that help retirees with winter heating costs and warning of painful cuts when the government rolls out its first budget next month. Things, Mr. Starmer said, “will get worse before they get better.”

As he prepares to address his party’s annual conference on Tuesday, several analysts said they expected Mr. Starmer to shift his tone — if not to one of hope and sunny optimism, then at least to one in which he will show how the government’s harsh early moves will pay off in the long term.

“He’ll hammer home the message that he inherited a legacy of ashes,” said Robert Ford, a professor of political science at the University of Manchester. “But then he’ll pivot to the big structural changes that will make Britain stronger.”

One problem for Mr. Starmer is that his austere public tone has coincided with signs that he can be more profligate in private. He has been dogged by a series of tempests over freebies accepted by him and his wife, Victoria, as well as by internal squabbling over the salary paid to his powerful chief of staff, Sue Gray, which exceeds that of the prime minister himself.

The dispute over his adviser’s pay, which was leaked to the BBC, has prompted a flood of coverage of a supposedly strife-torn Downing Street, where political aides and senior civil servants are said to be disclosing damaging information on their rivals. The staunchly pro-Conservative Daily Telegraph summed up the waspish atmosphere with the headline, “I’m Still in Control, Says Starmer, as Feud Erupts.”

By themselves, none of these issues add up to much. But taken together, they have scuffed Mr. Starmer’s reputation for competence and probity. London newspapers, many of which share The Telegraph’s pro-Tory tilt, have delighted in splashing unflattering headlines about how Labour Party donors paid for expensive eyeglasses for Mr. Starmer and for glamorous gowns for his wife.

“What is slightly surprising is the lack of awareness of their political vulnerability,” said Jill Rutter, a senior research fellow at U.K. in a Changing Europe, a research institute in London. “We’ve got a Tory press, and Keir Starmer has made so much of Tory sleaze over the last few years.”

Mr. Starmer and his allies defend his acceptance of gifts on various grounds: the free box seats for games of Arsenal, his favorite soccer team, are necessary because his security detail makes it impossible for him to sit in the stands.

The money for Ms. Starmer to buy clothes was appropriate, said David Lammy, the foreign secretary, because the prime minister and his spouse do not have a wardrobe budget and they need to “look their best for the British people.” (On Friday, however, the prime minister and other senior Labour ministers said they would no longer accept donations for clothing.)

Critics say the couple’s readiness to take freebies was at odds with Mr. Starmer’s oft-repeated pledge to preside over a government of service, after years of Conservative governments that were marred by scandals, incompetence and a sense of being out of touch with regular people.

“The first thing everyone learned about this Labour government is that they took money away from pensioners,” said Steven Fielding, an emeritus professor of political history at the University of Nottingham, referring to the cutback in subsidies given to older people to pay for heating fuel.

“In that context,” Professor Fielding said, “these things about Sue Gray’s pay, Keir Starmer’s free tickets, and his wife’s free clothes muddies the water. It suggests this is not such a different government.”

Mr. Starmer has taken pains to draw a line between his government and 14 years of Conservative rule. He excoriated his predecessors for leaving a 22 billion pound ($29.3 billion) “black hole” in the government’s finances, which he said made it necessary to curb the fuel subsidy for all but the poorest seniors.

He unveiled a review of England’s depleted National Health Service, which concluded that the system had been “starved of capital” under successive Conservative governments. He announced an emergency plan to release thousands of prisoners early to relieve a similarly neglected, overcrowded prison system.

“People have every right to be angry,” Mr. Starmer said in a characteristically chiding speech about the N.H.S.

Voters, however, are not taking out their anger only on the Conservatives. Mr. Starmer’s approval ratings have tumbled, as well. He was viewed favorably by 32 percent of people and unfavorably by 46 percent, according to a poll taken by the market research firm Ipsos in early September. That was his highest unfavorable rating since the Labour Party lost a special election in Hartlepool, a northern port city, in 2021 — a defeat so stinging that it put Mr. Starmer’s party leadership briefly at risk.

Whatever the hit to his popularity, Professor Ford argued, Mr. Starmer was right to emphasize the problems in the early days of his government to make it clear where the fault lies. He pointed out that Margaret Thatcher weathered a rocky first year with dire approval ratings. In a five-year term, he noted, Mr. Starmer will have time to shift the focus to how his policies had improved the country before he faces the voters again.

But other analysts said there was a danger of overdoing the misery. Professor Fielding noted that in 1945, a Labour prime minister, Clement Atlee, presided over one of the most consequential modern British governments, creating, among other things, the N.H.S. But his austere policies — he extended the wartime rationing of goods — soured the public, which turned Labour out of power six years later.

The downbeat message could also undercut the government’s efforts to lure foreign investment, a theme that is likely to feature in a speech at the conference on Monday by the chancellor of the Exchequer, Rachel Reeves.

“If you’re trying to attract more foreign investors to the U.K., and you’re saying, ‘We’re releasing people from jail because we have no room, our N.H.S. isn’t working, and we’re cutting fuel subsidies for old people,’ that’s not going to be very effective,” Ms. Rutter said. “There’s too much of pain for pain’s sake rather than, ‘Take the medicine now and things will get better in the long run.’”

A Russian military patrol plane breached Japanese airspace off the country’s northwestern coast three times on Monday, prompting Japan’s military to dispatch a fighter jet to issue radio warnings and, for the first time, to use a signal flare to deter the Russian aircraft.

According to Yoshimasa Hayashi, the chief cabinet secretary to Prime Minister Fumio Kishida, the Russian plane flew above Rebun Island, which is northwest of Hokkaido, Japan’s northernmost prefecture, between 1 p.m. and 3 p.m. on Monday afternoon.

“This violation of our airspace is extremely regrettable,” said Mr. Hayashi, in remarks to reporters on Monday afternoon. “We have lodged an extremely strong protest with the Russian government through diplomatic channels and have strongly urged them to prevent a recurrence.”

This was not the first time that a Russian military plane had violated Japanese airspace but it was the first time that Japan’s military had responded with a flare to warn the plane to leave. Last month, a Chinese military aircraft flew into Japan’s territorial airspace and the government said it was the first known incursion by the Chinese military.

Minoru Kihara, Japan’s defense minister, said Japan’s military had dispatched F-15 and F-35 fighter jets but that there had been “no particularly dangerous acts by the Russian aircraft.”

According to Japan’s defense ministry, the flights on Monday represented the 44th known incursion by a Russian plane — or an aircraft suspected to be Russian — since 1967, but it was the first time that a Russian military plane had breached Japanese territorial airspace since June 2019.

Mr. Kihara noted that both Chinese and Russian naval vessels had passed this week through the Soya Strait between Hokkaido and Sakhalin, a Russian island about 25 miles north of Hokkaido. Mr. Kihara said it was possible that the movement of the ships and the Russian aircraft were related.

Mr. Hayashi said the Japanese government did not know the “intentions and goals” of the Russian military aircraft. He said Japan would “take all possible measures to ensure vigilance and surveillance.”

The prime minister is in New York to attend the United Nations General Assembly, and Mr. Hayashi said he had advised Mr. Kishida to “respond calmly and resolutely” and to cooperate closely with the United States.

Russia’s embassy in Tokyo referred requests for comment to the defense ministry, which did not immediately respond.

Anton Troianovski contributed reporting from Berlin.

Christine Marlier was angry when President Emmanuel Macron called a snap election this summer. She’s even angrier now that he appointed a right-wing prime minister, despite the fact that a leftist bloc won the most seats in Parliament.

But Ms. Marlier left that anger behind at home in the far northeast of France when she boarded a bus for a four-hour ride to a nearly 100-year-old festival on the outskirts of Paris that celebrates left-wing politics in general, and French Communism in particular.

The Fête de l’Humanité — festival of humanity — is an unlikely mixture of Burning Man, Woodstock and a political convention.

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