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Moallem, who is visiting Moscow, suggested the deal could be acceptable in Damascus.
"Syria welcomes the Russian proposal out of concern for the lives of the Syrian people, the security of our country and because it believes in the wisdom of the Russian leadership that seeks to avert American aggression against our people," Moallem said in a statement.
The proposal was welcomed by the UN and a number of European governments. UN secretary general Ban Ki-moon said he would propose the security council unite and vote on an immediate chemical weapons transfer, placing weapons and chemical precursors in a safe place within Syria for international destruction.
Earlier, Ban said that he hoped that a forthcoming report by UN inspectors on the 21 August attack on a rebel-held area east of Damascus called Ghouta, which the US says killed more than 1,400 people, would spur the international community into action.
"Two and half years of conflict in Syria have produced only embarrassing paralysis in the security council," Ban said at a press conference.
The French government has said it would wait for the UN report, being prepared by a Swedish scientist, Åke Sellström, before making a final decision on taking part in military action.
The Sellström report is unlikely to come before the end of this week, diplomatic sources said. The samples brought back from a two-week visit are being studied in four European laboratories, to ensure that the result is conclusive.
In the British parliament, David Cameron responded positively but cautiously to Russia's move, saying if it was a genuine offer, it should be regarded as a big step forward.
Downing Street initially indicated that the Kerry proposal was not serious, pointing out that the idea had not been raised during the lengthy discussion on Syria at the G20 dinner in St Petersburg. They added that the focus should be on Assad's record with chemical weapons.
But in a Commons debate on the G20 and Syria, Cameron said it would be "hugely welcome" if the Assad regime were to hand over its chemical weapons stockpile.
Susan Rice, the US national security adviser, said that "even greater barbarism" would follow if the US did not take military action against Assad. "The decision our nation makes in the coming days is being watching in capitols around the world, especially in Teheran or Pyongyang," Rice told an audience at the New America Foundation in Washington on Monday.
Rice, the former US ambassador to the UN, did not address Russia's offer for Assad to relinquish his chemical stockpiles.
Additional reporting by Spencer Ackerman in Washington and Patrick Wintour in London