British Prime Minister David Cameron sought to win cooperation from Iran's President Hassan Rouhani against jihadists in Syria on Wednesday in the first meeting between the countries' leaders in 35 years.

A Downing Street spokesman said Cameron and Rouhani agreed that "all states in the region must do more to cut off support for all terrorist groups, including financial support" but stopped short of announcing any firmer cooperation.

"The prime minister and president noted the threat posed to the whole region by ISIL," said the British spokesman, using the acronym for the former Islamic State of Iraq and the Levant, since renamed the Islamic State (IS) group.

It was the first meeting between a British prime minister and Iranian president since the 1979 Islamic revolution, and took place at the British mission at the United Nations on the sidelines of the General Assembly.

Rouhani posted two photographs of himself with Cameron and wrote on Twitter: "One hour of constructive and pragmatic dialogue, new outlook."

"First meeting between UK and Iran heads of state in 35 years," he wrote. Cameron is head of the British government. Queen Elizabeth II is head of state.

Rouhani said Monday that the people in the region were "defending themselves... against the terrorists" and that Iran would help.

US President Barack Obama on Wednesday sought to rally widespread international support for US-led air strikes to defeat jihadists in Iraq and Syria.

The United States and Arab allies launched the first attacks against IS militants in Syria on Tuesday, expanding action the US has been leading against the jihadists in Iraq since the start of August.

Britain and France have taken up the task of trying to win some greater form of cooperation from Iran against IS.

- Britain presses Iran -

Tehran, which usually rails against any US presence in the Middle East, has been unusually accepting of the US action in Iraq, where it is also tackling IS.

But it is a also strong backer of the Syrian regime, which is fighting other rebel groups, some of them US-backed, all of which it regards as "terrorists".

Cameron welcomed Iran's support for the new government in Iraq and its efforts towards a more inclusive governance.

"He argued that a similar approach was needed in Syria, to promote a transition to a new government capable of representing all Syrians," the Downing Street spokesman said.

Downing Street said Cameron and Rouhani agreed to work to improve relations, which would help build mutual trust and agreed it was "vital to seize the opportunity of securing a comprehensive agreement" on Iran's nuclear program.

The British prime minister also raised the case of British-Iranian woman Goncheh Ghavami, 25, who was arrested in June when she went to a stadium to watch a men's volleyball game.

Cameron underlined "the impact that such cases had on Iran's image in the UK," the spokesman said.

While Rouhani's government advocates more social freedoms, Iranian conservatives want to strengthen measures to prevent men and women from mixing.

Cameron said the British parliament would hold an extraordinary session on Friday to vote joining the strikes, as requested by Baghdad.

He said he was "confident" the House of Commons would approve the action requested by Iraqi Prime Minister Haidar al-Abadi during a meeting between the two leaders at the UN General Assembly in New York.

He was last year defeated in the House of Commons over military action in Syria.