Britain's David Cameron and Russia's Vladimir Putin have agreed to re-start talks on finding a solution to the crisis in Syria, a statement from Cameron said on Monday.

The Russian president phoned Cameron to congratulate him on his re-election as prime minister and the two agreed that Syria talks should resume, a spokeswoman from Cameron's office said.

Past peace negotiations have failed to resolve a crisis in which Islamic State (IS) militants have seized swathes of territory in Iraq and Syria in a 4-year civil war that has killed 220,000.

"Both leaders agreed that it is in the interest of both the UK and Russia to help find a solution to the civil war in Syria and particularly to stop the rise of ISIL," another term for IS, a spokeswoman said.

"They agreed that their national security advisers should meet to restart talks on the Syrian conflict."

The two leaders also spoke about Ukraine, where fighting between government forces and pro-Russian separatists have killed thousands over the last year.

Cameron said they would "continue to have deep differences" on the war, in which Russia denies supporting the rebels with weapons and troops.

The Conservative leader, re-elected in May, said that the priority was to enforce a February peace deal agreed in Belarussian capital Minsk.

Cameron concluded the phone call by noting British and Russian cooperation on working for a nuclear deal on Iran.

The British leader expressed home that the two countries "could find other issues where the UK and Russia could work together on matters of mutual interest" in the years ahead, the spokeswoman said.