Iran's president has criticised "illegal" UN Security Council sanctions against his country, in a speech at the General Assembly in New York.
Mahmoud Ahmadinejad said debate over Tehran's nuclear programme was "closed" and the issue was now in the hands of the UN's nuclear watchdog, the IAEA.
French President Nicolas Sarkozy said a nuclear Iran could threaten the world.
Other issues raised by world leaders included Darfur, climate change, protests in Burma and human rights.
In a wide-ranging speech, Mr Ahmadinejad reiterated his assertions that all of his country's nuclear activities had been "peaceful and transparent".
Iran's nuclear work would be monitored by the International Atomic Energy Agency (IAEA), its "appropriate legal path", he added.
He denounced the "arrogant" and "bullying" permanent members of the UN's Security Council, which has imposed sanctions on Iran over its uranium enrichment programme.
And he offered educational programmes to help other UN member states with their own nuclear work.
Representatives of the US and Israel were absent for Mr Ahmadinejad's speech, in which he also repeated his verbal attacks on Israel as an "illegal Zionist regime".
In his speech, Mr Sarkozy said that while Iran had the right to nuclear energy, allowing Tehran to develop nuclear weapons would mean an "unacceptable risk" for regional and world stability.
There would be no world peace if the international community showed "weakness in the face of the proliferation of nuclear weapons", Mr Sarkozy said.
But there were dissenting views, among them Nicaraguan President Daniel Ortega, who asked how the US - the only country to have used nuclear weapons - could challenge the rights of Iran and North Korea to a peaceful nuclear programme.
US President George W Bush used his 15 minutes at the podium to highlight human rights violations around the world, highlighting Belarus, North Korea, Syria and Iran.
The central theme of President Bush's speech was the struggle against extremism.
He focused on the themes that have dominated much of his presidency - the need to spread freedom, to reward advocates of democracy and to isolate regimes whose policies run counter to what he sees as the tide of history.
Mr Bush contrasted those who were seeking the path of democracy: Lebanon, Iraq and those he dubbed moderate or mainstream Palestinian leaders, as opposed to the leadership of North Korea, Syria and Iran.
'Climate of change'
UN chief Ban Ki-moon told leaders the world faced "daunting challenges" - from tackling climate change to ending conflict in Sudan's western region of Darfur.
Addressing the general assembly for the first time as UN chief, Mr Ban called for "an internal climate of change" at the international body to deal with a "fractured world". He said the UN needed to adapt and focus not on rhetoric but on results.
He stressed that peace in the Middle East was vital to regional and world stability, and insisted that "no stone would be left unturned to end the tragedy in Darfur".
"I expect the year ahead to be among the most challenging in our history. And I am sure that, together, we can make it one of the most successful," he said.
He also called on Burma's military leaders to show restraint in the face of continued pro-democracy protests led by Buddhist monks.
This line was echoed by Mr Bush, who said Americans were "outraged by the situation in Burma".
He announced "tighter" economic sanctions against the junta and urged other nations to apply pressure.
The ritual of the general assembly allows each country's head of state or government - though some are represented by their foreign minister - to speak for 15 minutes.
There will be nearly 200 speeches over several days. Each country determines the issues that it wants to raise.
There is no agenda as such, but the speeches of key countries are closely watched for any evidence of an inflection or shift in their foreign policies.