David Cameron and President Putin can overcome differences on Syria to bring new momentum to efforts to stop the killing in Syria, the PM has said.
Mr Cameron said it was no secret he and the Russian president had disagreements over Syria, but they shared a common aim - to end the conflict.
Both wanted to keep Syria intact and get a transitional government in place, he said.
Mr Putin was at No 10 for talks ahead of the G8 summit in Northern Ireland.
Speaking after the meeting, Mr Cameron said they had discussed three issues - the "rules of the game for the world economy", particularly on tax and company ownership; working together more closely on issues like science and space, trade and investment; and the situation in Syria.
'Common ground'
He said it was "no secret" that the two leaders had disagreements over Syria.
But he added: "What I take from our conversation today is that we can overcome these differences if we recognise that we share some fundamental aims: to end the conflict, to stop Syria breaking apart, to let the Syrian people decide who governs them and to take the fight to the extremists and defeat them."
He added: "We will use the opportunity of having G8 leaders together to try and build on this common ground."
President Putin said he did not agree that efforts to secure peace talks had been "thwarted". The conflict could only "be resolved by political and diplomatic means", he said.
Along with the US, Moscow has been leading efforts to organise peace talks in Geneva next month but the Syrian opposition has not said whether it will attend.
On Friday, the US announced it would supply some rebels with direct military aid after seeing evidence of chemical weapons use by Syrian President Bashar al-Assad's regime.
Moscow is unconvinced about the evidence on chemical weapons and has said it will supply President Assad with advanced anti-aircraft missiles.
Mr Cameron said earlier that no decision had been taken on whether the UK would follow the US's lead but told the Murnaghan programme it was "right to send a very clear message to Assad that he shouldn't think he can just win this conflict in a military way".
He said there were "very dangerous" elements within the Syrian opposition, who he would like to see "driven out of Syria", but there were also moderate elements who supported a "free" and "pluralistic" system.
"If we don't work with those elements of the Syrian opposition, then we can't be surprised if the only elements of the Syrian opposition that are... actually making any progress in Syria, are the ones that we don't approve of," he said.
'Act of folly'
Earlier his Lib Dem deputy, Nick Clegg, told the BBC's Andrew Marr programme: "We clearly don't think it [arming the rebels] is the right thing to do now otherwise we would have decided to do it."
Lib Dem Chief Secretary to the Treasury Danny Alexander said the case was "not proven yet" that arming the rebels would make a difference and former Lib Dem leader Lord Ashdown said it would be "an act of very considerable folly" to do so.
Mr Cameron has also been under pressure from his own backbenchers to hold a vote in Parliament on the issue. He told Sky: "I never want to stand in the way of Parliament having a say one way or another... [but] we are not there yet, we have not made that decision."
Julian Lewis, Conservative MP for New Forest East, told BBC Radio 4's the World This Weekend it would be "very unwise" to arm the rebels "behind Parliament's back".
He also said arming the Syrian opposition, when it includes extremist elements, would be "suicidal" as it could mean chemical weapons being used by the regime falling into the hands of al-Qaeda.
MPs 'unease'
On the same programme, Conservative Business Minister Michael Fallon rejected suggestions Mr Cameron was "keen" to arm the rebels: "I don't think anyone's keen to do anything in the Syria situation."
He added: "It's got to be done, as far as possible, in negotiation. If there's any further action to be taken it's got to be done internationally, if it's to have any chance of success and yes, the House of Commons should certainly have a say if there's to be any new British action."
Shadow Foreign Secretary Douglas Alexander said there was "unease" across Westminster about arming the rebels and questioned how the government could stop weapons falling into the wrong hands.
"The G8 is a key window of opportunity for David Cameron to exert pressure on President Putin and it is vital that he uses the coming hours to do so," he said.
Two years of civil war in Syria has left an estimated 93,000 people dead.
The G8 summit - a meeting of eight global leaders to address international issues - takes place in Lough Erne, County Fermanagh on Monday and Tuesday.
Canada, France, Germany, Italy, Japan, Russia, the US and the UK will be represented.
Mr Cameron will also meet President Obama ahead of the summit.
Courtesy: BBC