President Biden began what is likely to be his last summit with global leaders as commander in chief on Monday, pushing for even stronger support of Ukraine despite the looming uncertainty of how President-elect Donald J. Trump might undo his efforts.

Just before the began in Rio de Janeiro, Mr. Biden authorized the first use of U.S.-supplied long-range missiles by Ukraine , U.S. officials said.

The decision reflected a sense of urgency to cement Mr. Biden’s legacy on one of his presidency’s biggest foreign policy challenges. Mr. Biden and his aides are in a race against time as they seek to bolster Ukraine before Mr. Trump — who has been highly critical of aid to Ukraine — takes power.

At the start of the G20 summit on Monday, Mr. Biden used one of his final moments on the global stage to encourage more world leaders to assist Ukraine.

“The United States strongly supports Ukraine’s sovereignty and territorial integrity,” Mr. Biden said during an event on hunger and poverty with world leaders including Russian foreign minister Sergey Lavrov. “Everyone around this table in my view should as well.”

But while Mr. Biden’s authorization of long-range weapons may help Ukrainian troops under fire in western Russia in the short-term, his decision was unlikely to change the trajectory of the war, according to American officials and military analysts.

The Ukrainian military now has a limited supply of the missiles. Firing a small number at targets in Russia would not make much of a difference to the overall war, analysts said.

But the missiles, known as ATACMS, could serve as a deterrent, discouraging North Korea from further assisting Russia.

“These ATACMS aren’t going to turn the tide of battle in Kursk,” John J. Sullivan, a former U.S. ambassador to Russia during the Trump and Biden administrations, said on Monday at the Council on Foreign Relations. “But it’s a step in the right direction.”

As Mr. Biden slowly deliberated the decision over the long-range weapons, Russia was also preparing.

Russia has moved most of its attack planes that fire long-range missiles and drop bombs to locations outside the range of the U.S.-supplied weapons, according to U.S. intelligence and defense officials.

The decision to allow the use of long-range strikes inside Russia stood in contrast to the more cautious approach Mr. Biden has taken on the war up to now.

Since the war started more than two years ago, Mr. Biden has sent billions of dollars in military aid to Ukraine to help repel Russia, but repeatedly hesitated when it came to offensive weapons, worried about provoking a wider conflict.

Several Republican lawmakers and some Democrats had been calling on Mr. Biden to give Ukraine broader latitude to use them.

“Should he have done it before? Absolutely,” said William B. Taylor Jr., a former U.S. ambassador to Ukraine. “It’s taken far too long for this decision to come. But I hope it’s not too late.”

The decision, he added, marks a pivotal point in Mr. Biden’s support for Ukraine.

“The Biden administration recognizes they’ve got a limited amount of time to have an effect,” said Mr. Taylor, vice president for Europe and Russia at the U.S. Institute of Peace. “This is what Biden will be remembered for: If he gave the Ukrainians everything possible to allow them to win.”

Mr. Biden’s aides have said in the past that rallying allies to support Ukraine in the weeks after Russia’s invasion is among the prouder efforts of his presidency. His timely warnings that Mr. Putin was poised to invade also won him lasting appreciation in Ukraine, even as European nations and even Ukraine’s government remained skeptical that an all-out war was coming.

But as the war ground on and the casualties mounted, views among Ukrainians hardened on Mr. Biden and his deliberative decision-making process. Ukrainians felt they were left in a long, cruel limbo with too few weapons to win the war and a lack of a diplomatic strategy to end the fighting.

The White House has stressed its commitment to Ukraine, while also weighing concerns in the American intelligence community that Russian retaliation for authorizing long-range strikes would outweigh the benefits.

But the recruitment of North Korean troops to help Russia in recent weeks has alarmed the administration and Mr. Biden’s decision also came the same day that Russia bombarded Ukraine’s power grid in one of the war’s largest attacks.

Jon Finer, Mr. Biden’s deputy national security adviser, declined to confirm the authorization of the long-range missiles on Monday, but noted that the United States had said it would respond to Russia’s decision to escalate attacks on Ukraine with North Korean reinforcements.

“If there are circumstances that evolve and change, you know, we will evolve and change to meet them and to allow the Ukrainians to continue to defend their territory and their sovereignty,” Mr. Finer said during a news briefing on the sidelines of the G20 summit.

Beside authorizing the long-range strikes, the Biden administration has been trying to move more quickly to provide military equipment and financial assistance for Ukraine already approved by Congress.

Despite the last-ditch scramble, it was clear at the G20 summit that Mr. Biden’s strategy in Ukraine, like his broader foreign and domestic policy vision, could soon be a thing of the past.

The move to empower Ukraine to attack deeper within Russia came in Mr. Biden’s final months in office, and was made with full awareness that U.S. foreign policy could soon be overhauled once Mr. Trump is in the White House.

While Mr. Biden has centered his presidency on defending U.S. allies, world leaders are well aware that Mr. Trump campaigned on an “America First” isolationist approach and has accused other nations of not contributing enough to security alliances.

Mr. Trump has also been deeply skeptical of U.S. aid to Ukraine and argued that its president, Volodymyr Zelensky, should have cut a deal and made concessions to Russia.

Mr. Trump’s return to the White House is undoubtedly hanging over the meeting in Rio, said Josh Lipsky, the senior director for the Atlantic Council’s GeoEconomics Center.

“Even before the election, for the past year this outcome was on every leader’s mind,” Mr. Lipsky said. “The primary focus for the U.S. is to show the rest of the world that this forum matters and the U.S. will remain engaged.”

Mr. Biden’s Latin America trip, which included a and a , amounted to one last diplomatic push of his foreign policy agenda — even as many of the participants shifted focus. Some of the world leaders who met with Mr. Biden during his diplomatic swan song seemed to already be looking to the next chapter.

“China is ready to work with the new U.S. administration to maintain communication, expand cooperation and manage differences,” China’s leader, Xi Jinping said at the beginning of his meeting with Mr. Biden in Peru.

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China’s leader, Xi Jinping, met with Mr. Biden in Lima on Saturday.Credit…Eric Lee/The New York Times

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The G20 summit also comes at a time when some U.S. allies, including Brazil itself, appear to be strengthening other global partnerships to offer a counterweight to the West, including the BRICS alliance of Brazil, Russia, India, China and South Africa, which recently added Iran, Egypt, Ethiopia, and the United Arab Emirates as members.

Brazil’s president, Luiz Inácio Lula da Silva, planned to meet with Mr. Xi during the summit amid heightened competition between the U.S. and China for economic influence in regions like South America.

Mr. Biden acknowledged his lame-duck status during brief remarks in the Amazon rainforest on Sunday as he traveled from Lima, Peru to the G20 summit.

“It’s no secret, that I’m leaving office in January,” Mr. Biden said, declining to mention Mr. Trump by name. “I will leave my successor and my country a strong foundation to build on, if they choose to do so.”

Michael D. Shear contributed reporting from Rio de Janeiro, Ana Ionova from Manaus, Brazil, Andrew Kramer from Kyiv and Eric Schmitt from Washington.