Iran's supreme leader Ali Khamenei said Thursday he supported the decision to extend talks with world powers in search of a nuclear agreement, after a missed deadline for a deal.

"For the same reason I was not opposed to the negotiations, I am not opposed to their extension," said Khamenei, who has the final say on Iran's foreign and domestic policy matters.

Tehran and world powers announced Monday that talks on a comprehensive nuclear agreement had been inconclusive and would be extended until June 30 next year.

"We will accept a fair and rational agreement," but Iran will oppose "any excessive demand," Khamenei said in a speech to leaders of the bassiji Islamist militia, broadcast live on state television.

"We know that it is the American government who needs this deal, and they will be the losers if there isn't one," he added.

"The guiding principle of the Islamic system is to fight against arrogance and the arrogant government of the United States," Khamenei said, using Tehran's designation for Western powers.

"We don't have a problem with America but with the excessive and tyrannical demands" of its government, he said.

A year ago, Khamenei said he was not "optimistic" about the negotiations between Iran and the P5+1 group of nations -- Britain, China, France, Russia, the United States and Germany.

He has nevertheless thrown his weight behind the thorny talks and acknowledged that Iranian negotiators were facing a "difficult mission".

On Tuesday, in his first comment since Iran and world powers missed a Monday deadline for a deal, Khamenei said on Twitter that Iran would not sink "to its knees".

In Thursday's speech, he insisted again that failure to reach an agreement would not spell disaster for Iran.

"If the negotiations fail, it will not be the end of the world, because our economy is one of resistance," he said.

He also hailed Iran's negotiators led by Foreign Minister Mohammad Javad Zarif, who he said had "resisted harassment".

A final agreement is aimed at ensuring Tehran will never develop nuclear weapons under the guise of its civilian activities, and would lift international sanctions that have crippled Iran's economy.

Iran denies that it is seeking the bomb and insists its nuclear activities are for solely peaceful purposes.