President Biden will attempt on Tuesday to focus global attention on the need to protect and nurture democracies, calling for the world to continue backing Ukraine and urging advanced nations to do more to bolster economies in the developing world.

In his third speech as president to the United Nations, Mr. Biden is expected to promote his administration’s achievements around the globe even as he confronts challenges at home: growing resistance to additional Ukraine aid, a looming government shutdown, inflation and listless approval ratings ahead of next year’s election.

The president’s speech on Tuesday is the centerpiece of a week of international diplomacy as the Biden administration confronts threats from Iran, tensions with Israel and the slow, grinding efforts by Ukraine to push back Russia’s invasion.

Mr. Biden arrives at the United Nations at a moment when he has asserted American leadership in world affairs and repaired many of the relationships that frayed under his volatile predecessor, Donald J. Trump. But with the next election looming and Mr. Biden effectively tied with Mr. Trump in early polling, many other nations will be greeting the president with uncertainty about his staying power.

“He will lay out for the world the steps that he and his administration have taken to advance a vision of American leadership that is built on the premise of working with others to solve the world’s most pressing problems,” said Jake Sullivan, the president’s national security adviser. “The president will talk about how those steps — how all of those steps he’s taken so far ladder up to a larger vision.”

After a long career in the Senate and as vice president, Mr. Biden enjoys a strong reputation among his peers and is seen as a committed internationalist fighting the tide of isolationism. While the chaotic withdrawal of forces from Afghanistan left sour feelings among many traditional American allies, Mr. Biden has restored some of his global reputation by rallying the West and other allies against Russia’s invasion of Ukraine, the seminal foreign policy crisis of his presidency so far.

He has also managed to stitch together a series of partnerships in the Indo-Pacific in the face of aggressive moves by China. He has bolstered relations with Australia, India, the Philippines and other nations in the region; elevated the standing of a bloc called the Quad, consisting of the United States, India, Japan and Australia; brought together the leaders of Japan and South Korea at Camp David for a three-way alliance that had long eluded Washington; and just last week cemented a strategic relationship with Vietnam during his first visit to Hanoi.

At the same time, America’s two major rivals appear weakened. President Xi Jinping of China looks less potent internationally as his country’s four-decade streak of economic growth flattens while President Vladimir V. Putin of Russia cannot even travel to the United Nations meeting or other major international gatherings because of an International Criminal Court arrest warrant for war crimes in Ukraine.

But with his approval ratings mired in the low 40s and Mr. Trump threatening to take his job back in the November 2024 elections, Mr. Biden’s domestic troubles loom large over this year’s gathering at the United Nations.

“Biden has lots of reasons to feel good about his standing on the world stage, but the U.S. domestic political situation continues to introduce uncertainty,” said James M. Goldgeier, a professor and former dean of the School of International Service at American University. “The 2024 presidential election and the potential return of Donald Trump to the White House creates a great deal of uncertainty about the ability of the United States to chart a stable international course forward.”

On Monday, Mr. Biden announced the release of five Americans who had been imprisoned in Iran, the culmination of a lengthy negotiation in which the United States agreed to unlock $6 billion in Iranian oil revenue and release five Iranians jailed for sanctions violations.

Mr. Biden will met with Prime Minister Benjamin Netanyahu of Israel on Wednesday, the first face-to-face meeting between the pair since tensions between them deepened. And on Thursday, Mr. Biden will host Volodymyr Zelensky, Ukraine’s president, at the White House for the third time.

Mr. Biden’s advisers have publicly expressed confidence that a bipartisan majority in Congress will once again approve Ukraine aid. But that approval appears likely to become tangled up in the ongoing congressional fight over the budget. That would be a blow to Mr. Biden’s vow to support Ukraine’s military resistance “for as long as it takes.”

Mr. Biden has been making that promise since the months before Russia invaded Ukraine in February of last year. It is at the heart of the president’s vision for a more robust foreign policy that aims to reverse Mr. Trump’s “America First” agenda.

“We see, at this point, more — a strong demand signal for more American engagement, for more American investment, for more American presence across all continents and all quarters of the world,” Mr. Sullivan said.

At the United Nations this week, Mr. Biden will argue that the same nations that came together to oppose Russia’s invasion of Ukraine need to focus their attention on the desperate economic fates of some of the world’s poorest countries, many of them in the southern hemisphere.

That message is a continuation of one Mr. Biden delivered at the meeting of the Group of 20 nations in New Delhi this month. And it is part of the president’s strategy to counter China’s influence in developing nations with its Belt and Road Initiative that helps poorer countries build ports, rail lines and communications networks.

At the Group of 20, Mr. Biden described his administration’s request to Congress for billions of dollars in funding for the World Bank and the International Monetary Fund to help leverage even more private support for developing countries. White House officials said nearly $200 billion in credit could flow into countries around the world in the years ahead.

In his speech to the General Assembly on Tuesday, Mr. Biden plans to challenge other countries to do more to support nations whose people are struggling in deep economic distress with little hope for the future.

Kori Schake, the director of foreign and defense policy studies at the American Enterprise Institute, said it was important for Mr. Biden to show up at the United Nations to explain American positions and policies.

Those explanations can help ease anxiety around the globe that the United States is committed to the kinds of engagement that many of its allies are looking for.

With the exception of protectionist trade policies, “he’s done an awful lot to deserve the relief most countries feel after the anxiety of the Trump administration,” said Ms. Schake, who served as a national security aide to President George W. Bush.

“But there’ll be hesitance still internationally,” she said, “because President Biden can’t actually reassure countries that their fear can’t materialize of a return to the presidency by Donald Trump.”