The Palestinian Authority's President Mahmoud Abbas has said Hamas would have no role in governing Palestinians and has affirmed his readiness to work with mediators to implement a Gaza peace plan.
The General Assembly overwhelmingly voted to let Mr Abbas address the world body with a video message.
Speaking to those gathered in New York, he said: "Hamas will not have a role to play in governance.
"Hamas and other factions will have to hand over their weapons to the Palestinian National Authority."
Mr Abbas said the militant group's 7 October attack on Israel did not represent his people and that he condemned antisemitism.
"Despite all that our people have suffered, we reject what Hamas carried out on 7 October - actions that targeted Israeli civilians and took them hostages - because these actions do not represent the Palestinian people, nor do they represent their just struggle for freedom and independence," Mr Abbas said.
In his pre-recorded speech, the Palestinian leader said he was ready to work with US President Donald Trump, Saudi Arabia, France and the United Nations to implement a Gaza peace plan adopted at a 22 September conference.
He said the plan could pave the way for a just peace and broader regional cooperation.
Watch: Abbas says Hamas 'will not have a role to play' in Palestinian rule
The 89-year-old Palestinian Authority president addressed the assembly three days after France led a special summit in which a slew of Western nations recognised a state of Palestine.
He called on all countries to recognise a Palestinian state and thanked those who had already made the move.
Mr Trump's administration adamantly rejected statehood and, in a highly unusual step, barred Mr Abbas and his senior aides from traveling to New York for the annual gathering of world leaders.
Israeli Prime Minister Benjamin Netanyahu has vowed not to allow a Palestinian state and far-right members of his cabinet have threatened to annex the West Bank in a bid to deny any prospect of true independence.
The Palestinian leader's addess came as the United States, despite its opposition to him, weighs whether to try to stop Israeli annexation of the West Bank.
French President Emmanuel Macron, despite his disagreements with Mr Trump on statehood, said that the US leader joined him in opposing annexation.
"What President Trump told me yesterday was that the Europeans and Americans have the same position," Mr Macron said in an interview jointly with France 24 and Radio France Internationale.
US special envoy Steve Witkoff said Mr Trump, in a separate meeting with a group of leaders of Arab and Islamic nations, presented a 21-point plan for ending the war.
"I think it addresses Israeli concerns as well as the concerns of all the neighbors in the region," he told the Concordia summit on the sidelines of the UN General Assembly.
"We're hopeful, and I might say even confident, that in the coming days we'll be able to announce some sort of breakthrough," he added.
A White House official told AFP that Mr Trump wants to bring the conflict "to an expeditious close" and that foreign partners from the meeting "expressed the hope that they could work together with Special Envoy Witkoff to consider the president's plan".
Mr Macron said the US proposal incorporates core elements of a French plan, including disarmament of Hamas and the dispatch of an international stabilisation force.
A French position paper seen by AFP calls for the gradual transfer of security control in Gaza to a reformed Palestinian Authority once a ceasefire is in place.
Indonesian President Prabowo Subianto, one of the leaders who met jointly with Mr Trump, said that the world's most populous Muslim-majority country was willing to offer at least 20,000 troops.
Mr Abbas's Palestinian Authority enjoys limited control over parts of the West Bank under agreements reached through the Oslo peace accords that started in 1993.
Mr Abbas's Fatah is the rival of Hamas, which controls Gaza.
However, Mr Netanyahu's government has sought to conflate the two.
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France and other European nations, while not joining Israeli and US efforts to delegitimise the Palestinian Authority, have said that it needs major reforms.
Mr Netanyahu will address the UN General Assembly tomorrow.
"At the General Assembly, I will speak our truth - the truth of the citizens of Israel, the truth of the (Israeli) soldiers, the truth of our nation," Mr Netanyahu said at Ben Gurion airport ahead of his departure, according to a statement from his office.
He also said he would meet with Mr Trump for a fourth time in Washington.
"I will discuss with him the great opportunities that our victories have brought, as well as our need to complete the goals of the war: to bring back all our hostages, to defeat Hamas and to expand the circle of peace that has opened up to us," Mr Netanyahu said.
