Russian President Vladimir Putin restated his opposition to any strike, saying it would destabilise the region.
US President Barack Obama said action was necessary in reaction to the use of chemical weapons in Syria.
A joint statement from the US and 10 other nations called for a strong international response.
The US government accuses President Bashar al-Assad’s forces of killing 1,429 people in a poison-gas attack in the Damascus suburbs on 21 August.
Mr Assad has blamed rebels for the attack.
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After two days of talks, the most powerful countries in the world were still unable to speak with one voice on Syria. The French President Francois Hollande has been a stalwart supporter of taking action. UK Prime Minister David Cameron and the Turkish Prime Minister Recep Tayyip Erdogan have also both firmly been in favour of action on Syria, as have the Saudis, long opposed to President Assad.
But the G20 host, President Vladimir Putin, has proved a formidable opponent and his claim is that the balance of opinion was behind him. Among G20 nations, India, Argentina, South Africa and Russia’s Security Council ally – China – are clearly against punitive strikes. Alongside them, others are also uneasy at military action without UN approval.
At his press conference, you could sense President Obama’s emotion, exhaustion and frustration. For all the intense lobbying behind the scenes, where it seems David Cameron has been playing a key role, there is still more work to be done to build the international coalition that Mr Obama wants.
China and Russia, which have refused to agree to a UN Security Council resolution against Syria, insist any military action without the UN would be illegal.
Mr Putin said the discussions about Syria on Thursday evening had gone on well past midnight.
He added that he had had a one-to-one meeting with Mr Obama in which they had discussed Syria.
Both men had listened to the other’s position but had not agreed, he said.
Mr Putin said he believed a majority of the populations in countries supporting military action were against it.
Meanwhile French President Francois Hollande, who has been a firm proponent of intervention, said he would await for a report from UN weapons inspectors before taking a decision on military action.
The inspectors’ findings are not due to be made public until the week beginning 15 September – possibly even later.
Also speaking at the end of the summit, Mr Obama said there was a “unanimous” view that chemical weapons had been used in Syria.
He also said most leaders present at the summit thought it was most likely that the regime of Mr Assad was responsible.
Mr Obama argued action was required even when the Security Council was paralysed, as the international consensus against the use of chemical weapons had to be upheld.
Obama says he had a “candid and constructive conversation” with President Putin
However, Mr Putin described the use of chemical weapons as “a provocation on the part of the militants who are expecting to get support from outside”.
British Prime Minister David Cameron said the UK had “made available additional evidence of cloth and soil samples which underline the now overwhelming picture of a war crime” on 21 August.
Mr Cameron said that, given the depth of international divisions, the “summit was never going to reach agreement”.
But he added that if there were only a response to the crisis through the UN Security Council, that would mean the UK “contracting out its morality and foreign policy to the potential of a Russian veto”.
While the UK, Canada and Turkey all support Mr Obama’s call for action, the only leaders at the G20 meeting to commit to force in Syria are the US and France.
Correspondents in St Petersburg say opponents of US military intervention appear to far outnumber supporters within the G20.
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What is the G20?
Formed in 1999, the “group of 20” comprises the 19 leading national economies, plus the EU.
The 2008 financial crisis and the rapid rise of China, India and Brazil has led the G20 to replace the G8 as principal global economic forum Leaders generally meet annually, with several other lower-level meetings each year
A joint statement from the US, Australia, Canada, France, Italy, Japan, Republic of Korea, Saudi Arabia, Spain, Turkey and the UK called for “a strong international response” over Syria.
Recognising that the UN Security Council had been paralysed over the issue, the statement added the “world cannot wait for endless failed processes that can only lead to increased suffering in Syria and regional instability”.
In his comments to reporters on Friday, Mr Obama did not make clear what he would do if the US Congress decided against military action in a vote expected next week.
A poll commissioned by the BBC and ABC News suggested more than one-third of Congress members were undecided whether or not to back military action – and a majority of those who had made a decision said they would vote against the president.
The US ambassador to the UN Samantha Power said that the US had “exhausted the alternatives” to military action.
She said that according to American estimates, the 21 August attack had “barely put a dent” in Syria’s chemical weapons stockpile.
Also on Friday, the UN appealed for more aid for people in Syria, and also for the estimated two million Syrians who have fled their country.
David Cameron: “This summit was never going to reach agreement on what action was needed on Syria”
UN humanitarian chief Valerie Amos told the BBC that donor countries should “look again” at their contributions and be “as generous as they can”.
Mr Cameron announced on Friday that some countries at the G20 had agreed measures to speed up the delivery of aid, including lifting bureaucratic obstacles such as custom rules.
He said earlier that the UK would give an additional £52m ($80m) in aid for Syria – much of it for medical training and equipment to help civilians targeted by chemical attacks.
However, correspondents point out that the delivery of aid is complicated by the need to negotiate with armed groups on the ground.
Meanwhile, on the ground in Syria, rebels have withdrawn after briefly entering an ancient Christian town north of Damascus, the main opposition alliance has said.
Free Syrian Army (FSA) units captured military positions outside Maaloula after heavy clashes with government forces and militiamen on Thursday.
Also on Friday, the US embassy in Lebanon said that it would be evacuating its non-essential staff.
The move was prompted by “threats to US mission facilities and personnel,” a statement said. The US Consulate General in the Turkish city of Adana is also withdrawing non-essential staff.
Source: BBC News