The G20 summit has agreed "important steps" to cut off terrorist financing and counter extremist ideologies, David Cameron has said.
The Prime Minister was speaking at a press conference after discussing counter-terrorism measures with Russian President Vladimir Putin.
He said he had urged Putin to work with the international community to support the transition in Syria away from President Bashar al-Assad, and had made it clear that he believes bombing moderate opposition groups in the country was a "mistake".
Everyone recognises the need for compromise over Assad's future, he added, and said he feels the "gap" on views about what that should be has now "reduced".
He said there are still "very big disagreements" with Putin over both Syria and Ukraine - but said the two countries should work together where there is agreement.
Russia said however, Britain should join forces in the fight against terrorism.
Speaking to the British Prime Minister on the sidelines of the G20 summit in Turkey, Vladmir Putin urged cooperation, saying Russia appreciates Britain's past work in fighting terrorism.
Acknowledging that relations between the nations were "not of the best", he told Cameron that Friday's terror attacks in Paris demonstrated the need for them to "join efforts in preventing terrorism".
"Russia has analysed the positive groundwork that you have done in the past and to look into the future as to the way we should develop our relations," he said.