Nearly 130 heads of state meet this week with the post-World War Two order under strain and with the UN itself struggling to remain relevant and weathering attacks from Trump, who has slashed America's contributions and withdrawn from dozens of UN bodies.
Chinese leader Xi Jinping, who last addressed the diplomatic jamboree via video in 2021, will skip New York in favour of one-on-one talks with Trump in Washington on Thursday, fuelling debate about the UN's relevance in addressing global crises.
Compounding the crisis of morale and finance are questions about the next leader of the 80-year-old organisation: Secretary-General Antonio Guterres completes his term at the end of 2026, with no clear frontrunner in the race to replace him.
The 15-member UN Security Council may hold high-level meetings on Ukraine, AI and the Middle East, including talks with Arab leaders, diplomats said.
More than a year into Trump's second term, "we would no longer say that the UN is in freefall, but we would say that it's stuck in an open-ended crisis", said Richard Gowan of the International Crisis Group.
The US avoided losing its vote at the assembly by paying $US725 million ($A1 billion) in contributions to the regular budget this week, but it still owes the organisation more than a billion dollars and makes ongoing demands for cuts and reforms.
The assembly meets shortly after several artificial intelligence industry leaders called for a co-ordinated slowdown of the development of the technology, warning that it could soon improve on its own and escape human control.
Guterres has said that AI will be a major topic, adding that countries pushing its frontiers should set up "common guardrails in order to avoid this race to the bottom that could lead one day to a gigantic disaster at the global level."
The secretary-general has long proposed global governance of AI. In 2023, the UN created an advisory body on the technology, with members including tech executives, government officials and academics.
The warning has put Guterres at odds with Trump, who dismissed AI risks as a "hoax," saying there is a "sick conspiracy" against it and that China would benefit from the doubt being cast on its development.
The Middle East will again be a focus of discussions, as the US-Israeli war on Iran continues to drive global inflation and destabilise the region. Recent gains by Houthi militants threaten shipping in the vital Bab el-Mandeb Strait and could further spike energy prices.
Peace talks remain stalled, however, as Iran and the US continue to exchange strikes and Trump threatens a major escalation of the war.
Iranian President Masoud Pezeshkian is scheduled to address the assembly on Wednesday.
Israeli Prime Minister Benjamin Netanyahu - wanted by the International Criminal Court over alleged war crimes and crimes against humanity in Gaza that Israel denies - will speak on Thursday.
Also on the agenda is Russia's war in Ukraine.
Ukrainian President Volodymyr Zelenskiy and Russian Foreign Minister Sergei Lavrov will address the General Assembly.
Zelenskiy will likely seek to shore up Ukraine's position ahead of what is expected to be another tough winter, diplomats said.
