President Assad’s forces are alleged to have deployed the deadly arsenal against civilians in late August, an accusation President Assad has assiduously denied, most recently during an interview filmed over the weekend with Journalist Charlie Rose for US broadcaster CBS.
Cameron however warned that Moscow’s proposal, tabled by Russian Foreign Minister Sergei Lavrov on Monday, must not distract the international community from making clear that the use of Sarin gas was unacceptable.
Speaking in London on Monday morning, US Secretary of State John Kerry muted the notion that action against Assad could be obviated if Damascus were willing to hand over its chemical weaponry.
Kerry dismissed the idea as likely unacceptable to Assad, however shortly after Lavrov announced: "If the establishment of international control over chemical weapons in that country would allow avoiding strikes, we will immediately start working with Damascus."
He added: "We are calling on the Syrian leadership to not only agree on placing chemical weapons storage sites under international control, but also on its subsequent destruction and fully joining the treaty on prohibition of chemical weapons."
Walid al-Moallem, the Syrian foreign minister, said he welcomed Moscow’s plan "based on the Syrian's government care about the lives of our people and security of our country".
In response to the developments, on Monday afternoon Cameron told the House of Commons: "I've only recently heard this announcement myself. If that were to be the case, it would be hugely welcome.
"If Syria were to put its chemical weapons beyond use under international supervision clearly that would be a big step forward and should be encouraged.
"I think we have to be careful though to make sure this is not a distraction tactic to discuss something else rather than the problem on the table. But if it's a genuine offer, then it should be genuinely looked at."
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Downing Street indicated that any future decision by the Assad regime to hand over weapons would not detract from the need for a robust reaction to the poison gas attacks which have already taken place.
"A chemical weapons attack has happened," said Cameron's official spokesman. "We are very clear about the judgment we have reached about the responsibility for that and that is why the central point about the need for a robust response remains.
"There is a general point about the benefits to the international community (if) measures are taken to put these types of weapons - against which there is a very clear international taboo as well as international law - out of circulation. Ridding the world of the threat of them would only be a good thing.
"But I would bring you back to the fact that it is the Assad regime that is responsible for the attacks that we saw on August 21. I don't think there is anything that should deflect us from noting that point."
Kerry's comments came after talks in London with Foreign Secretary William Hague, at the end of a whirlwind tour of European capitals to rally support for President Barack Obama's plan for "limited and proportionate" strikes against the Assad regime.
The US secretary of state was briefing Congress in Washington later today, ahead of a White House address by Obama tomorrow and a series of votes in Congress over the next few weeks.
Obama blames Assad for the deaths of more than 1,400 civilians, but failed to secure consensus on the need for a punitive response at last week's G20 summit, where Russian president Vladimir Putin said he remains convinced that the attack was conducted as a "provocation" by the Syrian opposition.
Kerry said he understood public concern at the prospect of military action in the wake of the experience in Iraq but insisted that it would be a very limited intervention.
"We are not talking about war. We are not going to war. We will not have people at risk in that way," he said.
"We will be able to hold Bashar Assad accountable without engaging in troops on the ground or any prolonged kind of effort in a very limited, very targeted, very short-term effort that degrades his capacity to deliver chemical weapons without assuming responsibility for Syria's civil war."
Asked what President Assad could do to avoid military action, Kerry said: "He can turn over every single bit of his chemical weapons to the international community in the next week." But he added: "He isn't about to do it and it can't be done, obviously."
Kerry said the US accepted that there was "no military solution" to the two-and-a-half-year Syrian civil war, but believed that Assad would not come to the negotiating table if he felt he could wipe out his opponents with chemical weapons.
While repeating that the UK would not take part in any military strike on Assad, Hague said: "Our Government supports the objective of ensuring there can be no impunity for the first use of chemical warfare in the 21st century. As an international community, we must deter further attacks and hold those responsible for them accountable."
Later, Cameron clashed with Ed Miliband over Syria in the House of Commons, accusing the Labour leader of "wriggling and quibbling" over last month's vote which blocked UK participation in any military action against Assad.
Miliband called for the creation of a Syria contact group - including countries sponsoring the Assad regime, as well as representatives of the rebels - with the aim of renewing pressure for peace talks
"Over the past months, you have failed to carry the House on the issue of arming the rebels. Again, 10 days ago you failed to carry the House or the country because people were not willing to go along with a rush to war," said the Labour leader.
"But you will undoubtedly carry the House and the country as you undertake the necessary diplomatic, political and humanitarian action needed for a long-term solution to alleviate the suffering of the people of Syria."
Cameron told MPs that he had reflected all of Labour's concerns in his motion for last month's vote, and said that their failure to back it showed that they were not "serious about Syria" but only about political positioning.
"They are wriggling and quibbling on the Opposition front bench," said the Prime Minister. "They could have done the difficult thing and right thing for the country, instead they chose the easy and simple thing that was politically convenient."
He added: "Britain will not be part of any military action. We will continue to press for the strongest possible response, including at the United Nations. We will continue to shape more urgent, effective and large-scale humanitarian efforts. And we will work for the peaceful, political settlement that is the only solution to the Syrian conflict."
Asked whether the Government was planning to send UK arms to opposition forces in Syria, Cameron's spokesman said: "It isn't on the cards."
Shadow chancellor Ed Balls said "jaws dropped" when Cameron ruled out UK military action on the back of the Commons defeat and insisted Labour would be prepared to look at the issue again if fresh evidence was presented.
He told Channel 4 News: "If there is evidence and the Prime Minister puts it back on the table, we'll look at it. But he's the Prime Minister, he's got to lead."