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Prime Minister David Cameron has held face-to-face talks with Iranian President Hassan Rouhani as part of a bid to revive the Syrian peace process.

The pair's meeting - which was brought forward from Tuesday - was at the United Nations summit in New York.

Downing Street said it was a "good, considered, thoughtful discussion" between the two leaders.

Efforts to engage Tehran in a push to end Syria's civil war have been spurred by a thaw in relations with the west.

The meeting was rescheduled after Mr Rouhani decided to cut short his attendance at the UN General Assembly to fly home for funerals of victims of the Hajj stampede, which killed at least 700 people.

They talked for 45 minutes, a Downing Street spokeswoman said.

She said the prime minister had said so-called Islamic State could not be defeated as long as President Assad was head of the regime in Syria - a key difference with president Rouhani's view - and she added "we need to find a way forward on that".

The spokeswoman said the discussions were at "a very early stage" but the two leaders had agreed to continue their discussions.

Close ally

Last month, the British embassy in Iran reopened nearly four years after it was closed after it was stormed by protesters during a demonstration against sanctions.

And in July, Tehran reached a deal with six world powers aimed at curbing its nuclear programme.

Iran has been a close ally of Syrian President Bashar al-Assad in recent years.

Mr Cameron is expected to drop his opposition to President Assad playing a role in any transitional government during talks with a number of leaders in New York.

But on Sunday he told reporters President Assad had "butchered his own people" and was "one of the great recruiting sergeants" for so-called Islamic State.

"He can't play a part in the future of Syria and that position hasn't changed," the PM continued.

"Obviously conversations about how we bring about transition are very important and that's what we need to see greater emphasis on."

Asked if he believed Mr Assad should face prosecution at the International Criminal Court, Mr Cameron said: "People who break international law should be subject to international law."

Analysis by Carole Walker, BBC political correspondent in New York

It is clear that Britain has had to accept that it may be necessary to allow Assad to stay on in some form of interim role if a longer-term solution is to be achieved, not least because of the need to remain in step with the United States.

The other factor in all this is the election of Jeremy Corbyn as Labour leader. The anti-war veteran is opposed to extending military action, though the shadow foreign secretary Hilary Benn has said Labour would look at any proposal to do so.

David Cameron has not even discussed the matter with the new Labour leader yet.

The government is well aware of the potential risks and consequences of any military mission in the Middle East and it seems the prime minister is carefully assessing the rapidly shifting political and military picture before reaching any decision on what Britain should do next.

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But Mr Rouhani said it was essential the regime stayed in place.

"If we are to succeed in defeating terrorism, the government in Damascus cannot be weakened. It must be able to carry on the fight," he said.

Mr Cameron is attending several sessions at the UN but will not join Mr Rouhani, US president Barack Obama, Russian president Vladimir Putin and China's Xi Jinping in making a keynote speech.

Labour leader Jeremy Corbyn criticised that decision.

"What matters now is a broad and comprehensive plan as the foundation for a political solution to the conflict and a new United Nations Security Council resolution," he said.

"That's why it is so disappointing that David Cameron isn't showing leadership and unlike other world leaders won't be speaking at the UN this week."

In his speech at the Labour Party conference, shadow foreign secretary Hilary Benn called on the prime minister to "strain every sinew" over Syria at the summit.