WASHINGTON—World leaders gathering this week for an annual United Nations meeting will confront persisting global problems such as Covid-19 and climate change, while grappling with new tensions and conflicts dividing U.N. members.

Diplomats and leaders attending the U.N. General Assembly in New York will also contend with the return to power of the Taliban and the humanitarian situation in Afghanistan, as well as the challenge posed by Iran under a new, hard-line president, Ebrahim Raisi.

President...

WASHINGTON—World leaders gathering this week for an annual United Nations meeting will confront persisting global problems such as Covid-19 and climate change, while grappling with new tensions and conflicts dividing U.N. members.

Diplomats and leaders attending the U.N. General Assembly in New York will also contend with the return to power of the Taliban and the humanitarian situation in Afghanistan, as well as the challenge posed by Iran under a new, hard-line president, Ebrahim Raisi.

President Biden is scheduled to address the General Assembly for the first time as president on Tuesday, planning to appear in person after last year’s virtual gathering.

“‘Authoritarians have used the pandemic as a pretext to violate human rights and tighten their grips. Democracy, human rights and the international rules-based order are under attack.’”

— Linda Thomas-Greenfield, U.S. envoy to United Nations

Under pressure from New York City, the U.N. is requiring that participants be vaccinated, but will rely on the honor system, a U.N. spokeswoman said. Diplomats arriving in the U.S. must submit a negative test for Covid-19, said Linda Thomas-Greenfield, the U.S. ambassador to the U.N.

U.S. officials have asked countries to avoid bringing large delegations.

Brazilian President Jair Bolsonaro, who had the coronavirus but has said he isn’t vaccinated, is scheduled to speak Tuesday, before other leaders.

The gathering this year takes place in the midst of new tensions including a diplomatic rupture between the U.S. and its ally France over a nuclear-submarine agreement. Australia, as part of the deal with the U.S. and the U.K., said it would cancel a multibillion-dollar contract to buy submarines from France. On Friday, France recalled its ambassadors to Washington and Australia.

French President Emmanuel Macron will address the U.N. on Tuesday, later than Mr. Biden. That schedule affords an opportunity for the two leaders to address the dispute, although Mr. Biden wasn’t expected to hold any formal meetings and will return to Washington after his speech, aides said.

China’s Xi Jinping and Russia’s Vladimir Putin aren’t expected to attend the gathering or address it directly, leaving the job to subordinates. Mr. Raisi is scheduled to speak later than Mr. Biden on Tuesday.

Mr. Biden, who has promised attention to international alliances, has rejoined the U.N.-organized Paris climate accord, reversed a move to exit from the World Health Organization, or WHO, and is campaigning for a U.S. seat on the U.N. Human Rights Council after the U.S. left the group under President Donald Trump.

In his address, Mr. Biden is expected to address the pandemic and climate change while pressing other governments—including the new Taliban regime and China—on rights issues.

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“Authoritarians have used the pandemic as a pretext to violate human rights and tighten their grips,” Ms. Thomas-Greenfield told reporters Friday in New York, adding, “Democracy, human rights and the international rules-based order are under attack.”

U.S. positions on climate, health and rights issues highlight tensions between Washington and Beijing. The Biden administration has pressed China to make commitments on greenhouse-gas emissions, to reveal more about the origin of the Covid-19 pandemic and to stop undermining the autonomy of Hong Kong and detaining Muslim minorities in the Xinjiang region, a campaign the Biden administration has called a genocide.

Mr. Biden will host a virtual summit Friday of the leaders of Australia, India, Japan and the U.S.—an informal alliance known as the Quad—as he prepares for his own global summit of democracies later this year.

As the U.N. gathering approached, some diplomats worried that a focus on governance and rights could complicate ties with authoritarian countries that share some U.S. interests.

“If you say ‘the West, and the rest,’ we pay a price with the ‘rest’ if we exaggerate our emphasis on democratic principles,” said John Negroponte, who served as U.N. ambassador under President George W. Bush. “If we make that a litmus test, it’s going to be difficult to forge useful ties” with countries that are important in other respects.

While Afghanistan is likely to be a topic in many U.N. meetings, the country’s new Taliban leadership is unlikely to have official representation. Some Taliban leaders face longstanding U.N. travel restrictions, and the world body hasn’t ruled on any new representation for the country. Ambassador Ghulam M. Isaczai, of the previous, U.S.-backed government, is expected to speak in the assembly hall alongside other heads of state and senior officials, diplomats said.

The U.N. meeting is unlikely to ease the deadlock over efforts to revive the nuclear deal between the U.S. and Iran after Mr. Trump withdrew from the agreement in 2018.

Diplomats are discussing the possibility of a meeting between Iran’s foreign minister and the remaining members of the 2015 nuclear deal—France, Germany, the U.K., Russia and China. The most that could realistically be expected is an agreement by Iran to fix a date for resuming the nuclear negotiations in Vienna, people familiar with the discussions said.

Iran’s foreign ministry spokesman said on Sunday that Tehran remained opened to a meeting in New York and that its foreign minister would in any case hold bilateral talks with his counterparts from the nuclear-deal talks. Iran has so far this year refused direct talks with the U.S.

Iran’s foreign ministry spokesman said on Sunday that Tehran remained opened to a meeting in New York and that its foreign minister would in any case hold bilateral talks with his counterparts from the nuclear deal talks. Iran has so far this year refused direct talks with the U.S.

The Vienna talks on restoring the nuclear deal have been put on hold since June, and Mr. Raisi has so far warded off Western pressure to fix a date to resume the negotiations.

Most countries are eager for progress on climate change, while differing on who should bear the burden of expensive changes.

Mr. Biden said Friday that the U.S. is working with the European Union on a pledge to reduce global methane emissions by nearly a third by 2030, and he encouraged other countries to sign on to the effort.

Several world leaders joined Mr. Biden virtually for the Major Economies Forum on Energy and Climate, an event that Mr. Biden revived before U.N.-organized climate negotiations scheduled for November in Glasgow.

A list of attendees for Friday’s forum didn’t include leaders from China, the world’s top emitter of greenhouse gases, or Canada and Germany.

Mr. Biden’s international climate envoy, John Kerry, has pressed China on carbon dioxide emissions, but Beijing has said the overall state of relations with the U.S. is hurting efforts to cooperate.

On Monday, U.N. Secretary-General António Guterres and U.K. Prime Minister Boris Johnson are set to lead a climate meeting of world leaders in New York before the Glasgow gathering. Mr. Biden isn’t expected to attend.

—Laurence Norman in Brussels, Timothy Puko in Washington and Aresu Eqbali in Tehran contributed to this article.

Write to William Mauldin at william.mauldin@wsj.com