UNITED NATIONS — Facing a swirl of conflicts and crises across a fragmented world, leaders attending this week’s annual United Nations gathering are being challenged: Work together, not only on front-burner issues but on modernizing the international institutions born after World War II so they can tackle the threats and problems of the future.

Secretary-General Antonio Guterres issued the challenge a year ago after sounding a global alarm about the survival of humanity and the planet: Come to a “Summit of the Future” and make a new commitment to multilateralism — the foundation of the United Nations and many other global bodies — and start fixing the aging global architecture to meet the rapidly changing world.

The UN chief told reporters last week that the summit “was born out of a cold, hard fact: international challenges are moving faster than our ability to solve them.” He pointed to “out-of-control geopolitical divisions” and “runaway” conflicts, climate change, inequalities, debt and new technologies like artificial intelligence which have no guardrails.

The two-day summit started Sunday, two days before the high-level meeting of world leaders begins at the sprawling UN compound at New York City. The General Assembly approved the summit’s main outcome document — a 42-page “Pact of the Future” — on Sunday morning with a bang of the gavel by the Assembly president, Philémon Yang, signifying consensus, after the body voted 143 to seven with 15 abstentions against considering Russian-proposed amendments to significantly water it down.

The pact is a blueprint to address global challenges from conflicts and climate change to artificial intelligence and reforming the U.N. and global institutions. Its impact will depend on its implementation by the assembly’s 193 member nations.

“Leaders must ask themselves whether this will be yet another meeting where they simply talk about greater cooperation and consensus, or whether they will show the imagination and conviction to actually forge it,” said the secretary-general of Amnesty International, Agnès Callamard. “If they miss this opportunity, I shudder to think of the consequences. Our collective future is at stake.”

This is the UN’s biggest week of the year.

The summit is the prelude to this year’s high-level meeting, held every September. More than 130 presidents, prime ministers and monarchs are slated to speak along with dozens of ministers, and the issues from the summit are expected to dominate their speeches and private meetings, especially the wars in Gaza, Ukraine and Sudan and the growing possibility of a wider Mideast war.

“There is going to be a rather obvious gap between the Summit of the Future, with its focus on expanding international cooperation, and the reality that the U.N. is failing in Gaza, Ukraine and Sudan,” said the UN director for the International Crisis Group, Richard Gowan. “Those three wars will be top topics of attention for most of the week.”

One notable moment at Tuesday’s opening assembly meeting: President Biden’s likely final major appearance on the world stage, a platform he has tread upon and reveled in for decades. At the upcoming meetings, the American ambassador, Linda Thomas-Greenfield, told reporters this week: “The most vulnerable around the world are counting on us to make progress, to make change, to bring about a sense of hope for them.”

To meet the many global challenges, she said, the American focus at the U.N. meetings will be on ending “the scourge of war.” Roughly 2 billion people live in conflict-affected areas, she said.

Last September, the war in Ukraine and its president, Volodymyr Zelensky, took center stage at the global gathering. As the first anniversary of Hamas’s deadly attack in southern Israel approaches on October 7, the spotlight is certain to be on the war in Gaza and escalating violence across the Israeli-Lebanon border, which is now threatening to spread to the wider Middle East.

Iran supports both Hamas in Gaza and Lebanon’s Hezbollah militants. Its new president, Masoud Pezeshkian, will address world leaders on Tuesday afternoon. President Mahmoud Abbas of the Palestinian Authority is scheduled to speak Thursday morning, and Israel’s prime minister, Benjamin Netanyahu, on Thursday afternoon.

Mr. Zelensky will get the spotlight twice. He will speak Tuesday at a high-level meeting of the Security Council — called by America, France, Japan, Malta, South Korea, and Britain — and will address the General Assembly on Wednesday morning.

Slovenia, which holds the council’s rotating presidency this month, chose the topic “Leadership for Peace” for its high-level meeting Wednesday, challenging its 15 member nations to address why the UN body charged with maintaining international peace and security is failing — and how it can do better.

“The event follows our observation that we live in a world of grim statistics, with the highest number of ongoing conflicts, with record high casualties among civilians, among humanitarians, among medical workers, among journalist,” the Slovenian ambassador, Samuel Zbogar, told reporters. He cited a record-high 100 million people driven from their homes by conflict.

“The world is becoming less stable, less peaceful, and with erosion of the respect for the rules, it is sliding into the state of disorder,” Mr. Zbogar said. “We have not seen this high need to rebuild trust to secure the future ever before.”

A key reason for the Security Council’s dysfunction is the division among its five veto-wielding permanent members. America, Israel’s closest ally, is a supporter of Ukraine alongside Britain and France. Russia invaded Ukraine and has a military and economic partnership with China, though Beijing reasserted its longstanding support for every country’s sovereignty without criticizing Russia in a recent briefing paper for the UN meetings.

President Macron of France and Britain’s new prime minister, Sir Keir Starmer, will be at the United Nations this week along with Mr. Biden. Presidents Putin of Russia and Xi of the People’s Republic of China are sending their foreign ministers instead. Neither Messrs. Putin nor Xi attended last year, either.

Mr. Guterres, who will preside over the whole affair this week, warned that the world is seeing “a multiplication of conflicts and the sense of impunity” — a landscape where, he said, “any country or any military entity, militias, whatever, feel that they can do whatever they want because nothing will happen to them.”

He rued what he called “the fact that nobody takes even seriously the capacity of the powers to solve problems on the ground.” 

Associated Press