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US Secretary of State John Kerry "lost an argument" to back diplomatic efforts in Syria with a serious threat of military force.

Kerry expressed his frustration at his own government for not intervening more forcefully, as talks to bring an end to the bloodshed continued to fail.

His complaints were heard at a meeting with a small group of Syrian civilians, a recording of which was leaked to The New York Times.

"I think you're looking at three people, four people in the administration who have all argued for use of force, and I lost the argument," Kerry said.

"We’re trying to pursue the diplomacy, and I understand it’s frustrating. You have nobody more frustrated than we are."

The meeting took place at the Dutch Mission to the UN on September 22, after the ceasefire spearheaded by Kerry between the US and Russia collapsed.

In the days that followed heavy bombing on rebel-held areas of Aleppo by regime forces killed 338 people, including 100 children, according to the World Health Organisation.

Efforts to broker another pause in fighting have so far been rejected by Bashar al-Assad’s government.

The approximately 20 participants at the meeting included representatives of four Syrian groups that provide education, rescue and medical services in rebel-held areas and diplomats from three or four countries, The Times said.

The recording was made by a non-Syrian attendee, and several other participants confirmed its authenticity.

In the audio clip posted on the newspaper’s website, the group pressed Kerry on what they saw as contradictions in US policy.

One woman, Marcell Shehwaro, asked "how many Syrians" had to be killed to prompt serious action.

"A lot of Americans don't believe that we should be fighting and sending young Americans over to die in another country."

Kerry responded that "Assad's indifference to anything" could push the Obama administration to consider new options, but he also said that "any further American effort to arm rebels or join the fight could backfire".

"The problem is that, you know, you get, quote, enforcers in there and then everybody ups the ante, right? Russia puts in more, Iran puts in more; Hezbollah is there more and Nusra is more; and Saudi Arabia and Turkey put all their surrogate money in, and you all are destroyed," he said.

He said Congress would never agree to use military force, adding: "A lot of Americans don't believe that we should be fighting and sending young Americans over to die in another country."

At the end of the meeting, he reiterated a long held view that the best outcome of the civil war, now in its sixth year and claimed 400,000 lives, was a political solution.

He said: "You can have an election and let the people of Syria decide: Who do they want?"

"Everybody who's registered as a refugee anywhere in the world can vote. Are they going to vote for Assad? Assad’s scared of this happening."

Russian forces joined the Syrian war a year ago, tipping the balance of power in favour of Assad, who is also supported by Iranian ground forces and Shi'ite militia fighters from Lebanon and Iraq.

The Times said State Department spokesman John Kirby declined to comment on what he described as a private conversation.