British Prime Minister David Cameron and Russian President Vladimir Putin made a 30-minute phone call on Monday, focusing their talks on Syria and Ukraine.

Putin also took the chance to congratulate Cameron on his "major success" in the British general election, a Downing Street spokesperson said following the phone call.

On Syria, the two leaders agreed that it is in the interest of both Britain and Russia to help find a solution to the civil war in Syria and particularly to stop the rise of the Islamic State (IS).

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

"The Prime Minister reiterated his belief that President Assad could not be part of the solution in Syria. And they agreed that both countries should continue talks with the moderate Syrian opposition as part of this effort," the unnamed spokesperson said in a statement.

Earlier this month, Putin, in a joint statement signed with Chinese President Xi Jinping, reiterated that they support Syria's sovereignty, unity and territorial integrity, regard political means as the only way to solve the crisis, and oppose any attempt of military intervention.

On Ukraine, Cameron said that they would continue to have "deep differences," but the priority now must be to deliver "full implementation of the Minsk agreement."

"The Prime Minister concluded the call by noting that the UK and Russia had worked successfully together on the Iranian nuclear issue and he hoped that in the years ahead, we could find other issues where the UK and Russia could work together," the spokesperson added.