David Cameron will tell Barack Obama in the White House on Monday that he believes Vladimir Putin may be prepared to adopt a more flexible approach on Syria.

The prime minister will tell the president, in talks being convened ahead of the G8 summit in Northern Ireland for June, that he was greatly encouraged by his meeting with Putin at the Black Sea resort of Sochi on Friday.

A bilateral meeting between Cameron and Putin, attended only by their respective national security advisers, overran after being dominated by Syria. Cameron was struck when the Russian president made a point of moving his briefing notes to one side and asking to hear the prime minister's thoughts on the Syrian crisis.

Britain has been insistent for months that the Syrian crisis, which has claimed at least 70,000 lives, can only be solved if the Syrian president, Bashar al-Assad, is removed from power. Russia has been supportive of the regime and has vetoed a series of UN security council resolutions critical of Assad.

Speaking during his flight to Washington, Cameron described his talks with Putin as "extremely positive and good". He said: "I was very heartened that while it is no secret that Britain and Russia have taken a different approach to Syria I was very struck in my conversations with President Putin that there is a recognition that it would be in all our interests to secure a safe and secure Syria with a democratic and pluralistic future and end the regional instability.

"We have a long way to go. But they were good talks and I am looking forward to now taking them up with President Obama and seeing if we can turn this proposal for a peace process and a peace conference into something that can make a real difference."

The prime minister has previously expressed immense frustration that Russian has repeatedly vetoed UN security council resolutions that were critical of the Assad regime. But No 10 believes that a major step was taken when the US secretary of state, John Kerry, and his Russian counterpart, Sergei Lavrov, agreed to convene a peace conference on Syria.

British sources say a great deal of work remains to be done and that Russia is far from abandoning support for the Assad regime. But the prime minister has high hopes for the peace conference, which is designed to involve Syrian rebels and representatives of the Assad government.

Cameron said he would use his meeting with Obama to "try to really put flesh on the bones of this plan for a peace conference and to think of all the things that would make it work and deliver a peaceful transition in Syria. A lot of progress has been made and I want to push on on that."

The prime minister, who is pushing with the French for the EU arms embargo on Syria to be lifted later in May, said Britain and the US were at one in wanting to help the rebels. Britain has provided non-lethal equipment to the rebels. Obama has faced criticism for refusing to arm the rebels though the US is co-ordinating weapons deliveries from Gulf states.

Cameron said: "There is very strong unity of purpose between Britain and America that we should be working closely with the rebels. It is important that we work with and shape what they are doing. I have always been in favour of that sort of engagement. That is why we are now giving them technical assistance. But I also think there is something bigger happening here which is a realisation that it would be far better if what we could do is bring about a political transition through a greater engagement and agreement between America, Russia, Britain, France and other powers."

Britain believes lifting the EU arms embargo would increase the pressure on the Assad regime, forcing the regime question whether its military dominance can last.