Leaders at the G8 summit in Enniskillen, Northern Ireland, are close to signing a joint statement on Syria, despite their differences.
Russia and the US are backing opposite sides in the conflict, but officials say the statement could soon be agreed.
This could include the proposed peace conference in Geneva, and more access for deliveries of humanitarian aid.
The summit, which is now in its final day, is also discussing tax evasion and efforts to boost trade.
Russian Deputy Foreign Minister Sergei Ryabkov said Moscow would sign up to the statement on Syria later on Tuesday.
But he stressed the Kremlin wanted each of the Syrian sides in the talks to select not only their own delegations but the future terms of any transitional government.
Sergei Ryabkov sidestepped the question of whether this could leave open a role for President Bashar al-Assad in the future.
Leaders at the G8 summit in Enniskillen, Northern Ireland, are close to signing a joint statement on Syria, despite their differences
To try to get as much consensus as possible on Syria, UK Prime Minister David Cameron – who is hosting the summit – held a working dinner on Monday night.
The leaders were alone, with no officials present, allowing them to express their views frankly.
After the meeting, British officials appeared more optimistic that an agreement could be reached on the joint statement on Syria.
However, they said it would take more work to agree the precise language.
Earlier on Monday, the British had raised the possibility of the other G8 nations issuing an end-of-conference statement without the participation of Russia.
But it now seems that Vladimir Putin is willing to consider some kind of joint stance, according to officials.
The communiqué is likely to back the launch of Syrian peace negotiations in Geneva, and insist that humanitarian aid agencies like the Red Cross are given access to all parts of the country.
Any statement which emerges may not be all that ambitious, correspondents warn – and even then, it is far from certain that any agreement will change the appalling reality in Syria itself.
The White House announced last week that it would provide military aid to the Syrian rebels. Russia meanwhile supplies weapons to the government of President Bashar al-Assad.
Presidents Barack Obama and Vladimir Putin met for an hour of bilateral talks on Monday, and at a sombre press conference afterwards it was clear they had had a difficult exchange.
Both presidents acknowledged their differences but said they shared a common desire to stop the bloodshed.
Presidents Barack Obama and Vladimir Putin have acknowledged at the G8 meeting in Northern Ireland that they have a different stance on Syria, but agreed to push for a summit in Geneva.
After face-to-face talks, Barack Obama and Vladimir Putin said they shared a common desire to end the violence.
Both also said they were optimistic on Iran, after its presidential election.
Earlier, the G8 nations discussed the global economy, with the leaders agreeing world prospects remained weak.
The G8 leaders are now heading to a working dinner, where Syria is likely to be top of the agenda.
Other nations joining the UK, US and Russia for the 39th Summit of the Group of Eight (G8) in Lough Erne, County Fermanagh, are Canada, France, Germany, Italy and Japan.
Vladimir Putin and Barack Obama met for about two hours on the sidelines of the summit.
Correspondents say that both leaders looked tense as they addressed journalists afterwards, with the Russian president regularly looking at the floor.
Vladimir Putin said: “Our positions do not fully coincide, but we are united by the common intention to end the violence, to stop the number of victims increasing in Syria, to resolve the problems by peaceful means, including the Geneva talks.”
Barack Obama said the two leaders had instructed their teams to press ahead with trying to organize the peace conference in Switzerland.
Neither the rebels nor the Syrian government have yet fully committed to the proposed Geneva talks, which would seek to end more than two years of unrest that has left an estimated 93,000 people dead.
Barack Obama and Vladimir Putin did say that they had agreed to meet in Moscow in September.
Earlier UK Prime Minister David Cameron, who is hosting the summit, had said he hoped to find “common ground” on Syria.
The US said last week it was prepared to arm opposition forces, saying it had evidence that Syrian President Bashar al-Assad’s forces had used chemical weapons on a “small scale”.
David Cameron, who backed the recent lifting of EU arms sanctions against the rebels, said on Monday that no decision had yet been made on whether the UK would do the same.
In an interview in Germany’s Frankfurter Allgemeine Zeitung on Monday, President Bashar al-Assad denied that his military had used chemical weapons, and warned that arming the rebels would result in “the direct export of terrorism to Europe”.
“Terrorists will return to fight, equipped with extremist ideology,” he said.
US President Barack Obama and Russian President Vladimir Putin at the G8 summit in Northern Ireland
On Monday, Russian foreign ministry spokesman Alexander Lukashevich said of the possibility of a no-fly zone over Syria: “I think we fundamentally would not allow this scenario.”
The formal talks on Monday covered the global economy.
In their statement after the session, the leaders said prospects remained weak but added that action in the US, Japan and eurozone had helped ease the situation.
“Downside risks in the euro area have abated over the past year, but it remains in recession.
“The US recovery is continuing and the deficit is declining rapidly in the context of a continuing need for further progress towards balanced medium-term fiscal sustainability.”
Ahead of the first session, the US and EU members of the G8 announced that negotiations were to begin on a wide-ranging free-trade deal.
David Cameron, Barack Obama and European Commission President Jose Manuel Barroso held a press conference on the proposed EU-US deal.
The British prime minister said a successful agreement would have a greater impact than all other world trade deals put together.
“This is a once-in-a-generation prize and we are determined to seize it,” said David Cameron.
He said the deal “could add as much as £100 billion [$157 billion; 117 billion euros] to the EU economy, £80 billion to the US economy and as much as £85 billion to the rest of the world”.
Barack Obama said the deal was a priority for the US and he hoped that it would create an economic alliance as strong as the diplomatic and security alliances the two sides enjoyed.
G8 Summit agenda
- 15:45: Official arrivals
- 16:45: Global economy
- 18:15: Bilateral meetings
- 20:00: Foreign policy
- 07:00: Bilateral meetings
- 08:30: Counter-terrorism
- 10:30: Tax transparency
- 14:30: Closing talks
- 15:30: UK PM press conference
- 15:45: Other leaders’ press conferences
(All timings BST)