US President Barack Obama has urged fellow world leaders to support Israeli-Palestinian peace negotiations currently under way.
He was speaking at the 65th UN General Assembly at the organisation's New York headquarters.
The week-long diplomatic marathon comes on the heels of a development summit which ended with a US pledge to revamp its foreign aid policy.
Leaders will also hold dozens of extra meetings on the sidelines.
Peace-keeping in Somalia, the possible break-up of Sudan, the conflict in Yemen, climate change and UN reform are all set to feature in these fringe meetings, which our diplomatic correspondent Jonathan Marcus says constitute the most important business of the event.
While the Millennium Development Goals summit - which was was also held in New York - had a clear focus, this meeting is more of a free-style event, says our diplomatic correspondent.
In one encounter on the Assembly's sidelines, Mr Obama met Chinese Premier Wen Jiabao and praised the two countries' collaboration on issues such as the economy, nuclear non-proliferation and regional security, while emphasising that economic challenges remained.
At the UN General Assembly, leaders take to the stage to make speeches on a subject of their choice.
Speaking shortly after UN Secretary General Ban Ki-moon launched the diplomatic marathon, the US president urged the audience to support Israeli-Palestinian peace negotiations which started on 2 September.
"We have travelled a winding road over the last 12 months, with few peaks and many valleys," Mr Obama said.
"But this month, I am pleased that we have pursued direct negotiations between Israelis and Palestinians in Washington, Sharm el-Sheikh and Jerusalem."
He said those longing for an independent Palestine must not try to tear down Israel, and called on Israel to extend a moratorium on building new settlements in the West Bank and East Jerusalem.
"Israel's settlement moratorium has made a difference on the ground, and improved the atmosphere for talks... We believe that the moratorium should be extended."
Mr Obama accepted that many remained pessimistic about the peace process, with cynics saying the two sides were too distrustful of each other, and too divided internally, to forge lasting peace.
"Rejectionists on both sides will try to disrupt the process, with bitter words and with bombs," he said. "Some say that the gaps between the parties are too big; the potential for talks to break down is too great; and that after decades of failure, peace is simply not possible."
But the US president called on his fellow leaders to consider the alternative.
"If an agreement is not reached, Palestinians will never know the pride and dignity that comes with their own state. Israelis will never know the certainty and security that comes with sovereign and stable neighbours who are committed to co-existence.
"The hard realities of demography will take hold. More blood will be shed. This Holy Land will remain a symbol of our differences, instead of our common humanity."
"Peace must be made by Israelis and Palestinians, but each of us has a responsibility to do our part as well."
'No peace without justice'
Speaking later on Thursday, Iran's President Mahmoud Ahmadinejad provoked a walkout from the UN's main chamber by the US and other delegates.
Mr Ahmadinejad said some saw the 11 September 2001 attacks on the US, which killed nearly 3,000 people, as part of a US conspiracy to protect Israel.
"The majority of the American people as well as most nations and politicians around the world agree with this view," he said.
He also repeated Iran's denial that it is seeking the capacity to build nuclear weapons.
Some members of the UN Security Council, he said, have "equated nuclear energy with nuclear bombs".
Iran has already endured four rounds of increasingly punitive economic sanctions over the dispute.
Foreign ministers from countries including the US, UK, China, France, Germany and Russia discussed the issue at a meeting on Wednesday, and it is also likely to be raised on the fringes of the General Assembly.
In his opening address, Mr Ban urged the nations to stand together in a time of growing challenges and uncertainty.
He said the UN provided a moral compass for a world in which social inequalities were growing, with women and children bearing the brunt.
He called for a "stronger UN for a better world".
"There can be no peace without justice," he said. "Let us send a clear message: No nation large or small can violate the rights of its citizens with impunity."
Mr Ban said the UN had embraced an ambitious agenda for a more prosperous world free of poverty, and for a greener, safer world free of nuclear weapons.