David Cameron has met Russian president Vladimir Putin for talks on the fringe of the G20 summit in Mexico which are thought to have focused on the situation in Syria.
The prime minister told Mr Putin that he wanted to seek "unity" behind achieving a political transition to a new government for the troubled Middle Eastern state.
Russia has been a staunch ally of President Bashar Assad and has been accused of blocking international action to prevent him clamping down on the uprising against his rule.
But Britain has welcomed Mr Putin's proposal for an international conference on Syria, while opposing his suggestion that Iran should be invited.
Mr Cameron said he also wanted to discuss talks being held in Moscow over Iran's nuclear ambitions.
Speaking as talks began in the Russian President's hotel in Los Cabos, Mr Cameron said: "I want to see us strengthen British-Russian relations. I think our economic relations are strong, with investment both ways and I want to see that encouraged.
"But... there are many international issues we should also discuss - talks that are taking place in Moscow over the future of the Iranian nuclear programme.
"And also the terrible situation in Syria and the need to seek unity to try to achieve transition there."
Relations between the UK and Russia have thawed somewhat under Mr Cameron, after a lengthy chill following the murder of dissident Alexander Litvinenko in London.
Mr Putin said today that the relationship was "developing quite positively", but made clear that differences remain.
"I would like to note that relations between Russia and Great Britain are developing and in my opinion they are developing quite positively," he said.
"However, we have things to discuss both about the international agenda and concerning our bilateral and in particular economic ties, which no doubt require special attention and our monitoring."