By John Irish and Khaled Yacoub OweisPARIS/AMMAN (Reuters) - Syria accepted a Russian proposal on Tuesday to give up chemical weapons and win a reprieve from U.S. strikes, while its warplanes bombed rebel positions in Damascus for the first time since the West threatened military action.The Russian diplomatic initiative, which apparently emerged from off-the-cuff remarks by the U.S. secretary of state, marks a sudden reversal after weeks in which the West appeared finally headed towards intervention in a two-and-a-half year old war.France said it would put forward a U.N. Security Council draft resolution for Syria to give up its stockpiles of chemical arms, threatening "extremely serious" consequences if Syria violates its conditions.Syria's rebels reacted with deep dismay to the proposal, which would halt Western military action to punish President Bashar al-Assad's forces for a poison gas attack that killed hundreds of people in a Damascus suburb last month.U.S. President Barack Obama, for whom the proposal provides a way out of ordering unpopular strikes days before contentious Congressional votes, said it could be a "breakthrough".Russia's Interfax news agency quoted Syrian Foreign Minister Walid al-Moualem, visiting Moscow, as saying Damascus had agreed to the Russian initiative because it would "remove the grounds for American aggression".While the diplomatic wrangling was under way in far-flung capitals, Assad's warplanes bombed rebellious districts of Damascus on Tuesday for the first time since the August 21 poison gas attacks. Rebels said the air strikes were a demonstration that the government now believed the West had lost its nerve."By sending the planes back, the regime is sending the message that it no longer feels international pressure," activist Wasim al-Ahmad said from Mouadamiya, one of the districts of the capital hit by the chemical attack.The war has already killed more than 100,000 people and driven millions from their homes, and threatens to spread violence across the Middle East.The Russian proposal "is a cheap trick to buy time for the regime to kill more and more people," said Sami, a member of the local opposition coordinating committee in the Damascus suburb of Erbin, also hit by last month's chemical attack.French officials said their draft resolution was designed to make sure the Russian proposal would have teeth, by allowing military action if Assad is uncooperative."It was extremely well played by the Russians, but we didn't want someone else to go to the U.N. with a resolution that was weak. This is on our terms and the principles are established. It puts Russia in a situation where they can't take a step back after putting a step forward," said a French diplomatic source.The Russian proposal makes it easier for members of the U.S. Congress to vote to authorize action as part of a diplomatic initiative, without it leading directly to missile strikes.Republican Senator John McCain, a leading hawk, said lawmakers were working on new wording of a Congressional resolution to ensure "strict timelines and guidelines that would have to be met" for Assad to give up chemical arms WELCOME WRENCH?Russia's proposal apparently began life as an off-the-cuff remark by U.S. Secretary of State John Kerry on Monday, although both Moscow and Washington later said President Vladimir Putin had discussed the idea in principle with Obama in the past. Putin's spokesman said it came up at a summit last week.With veto-wielding China also backing it, it would be the rare Syria initiative to unite global powers whose divisions have so far blocked Security Council action. Assad's main regional backer Iran has also signaled support, as has U.N. Secretary-General Ban Ki-moon.Washington and Paris have threatened to carry out strikes to punish Assad for the August 21 poison gas attack on Damascus suburbs, which they say Syrian government forces carried out.But after 12 years of wars in Iraq and Afghanistan, Obama has had a hard time winning over the public or members of Congress. Britain quit the coalition threatening force after Prime Minister David Cameron lost a vote in parliament.Moscow unveiled its proposal on Monday after Kerry, speaking in London, said the only way to halt strikes would be for Assad to give up his chemical arsenal. The State Department said his remarks were rhetorical and not meant as a serious proposal.But hours later Russian Foreign Minister Sergei Lavrov called for Assad's government to do just that.Responding to the Russian initiative, Obama told CNN: "It's possible that we can get a breakthrough," although he said there was a risk that it was a further stalling tactic by Assad."We're going to run this to ground," he said. "John Kerry and the rest of my national security team will engage with the Russians and the international community to see, can we arrive at something that is enforceable and serious."Robert Danin, a Middle East specialist and senior fellow at the Council on Foreign Relations, said the initiative spoils Obama's strategy, but Washington was likely to be relieved."It basically throws a bit of a wrench into the administration's plans, but it may be a welcome wrench."The wavering from the West was a blow for the Syrian opposition, which had thought it had finally secured military intervention after pleading for two and a half years for help from Western leaders that vocally opposed Assad.The Russian proposal "fails to hold the Assad regime responsible for the killing of innocents," the Syrian National Coalition said, calling it "a political maneuver which will lead to pointless procrastination and will cause more death and destruction to the people of Syria, and further threats to the countries and people of the region."Assad's forces - which had been withdrawing from fixed positions and bracing for expected Western strikes - appear to have responded to the hesitation by redoubling an offensive to clear fighters from Damascus suburbs.Troops and pro-Assad militiamen tried to seize the northern district of Barzeh and the eastern suburb of Deir Salman near Damascus airport, working-class Sunni Muslim areas where opposition activists and residents reported street fighting.Fighter jets bombed Barzeh three times and pro-Assad militia backed by army tank fire made a push into the area. Air raids were also reported on the Western outskirts near Mouadamiya.Syria is not a party to international treaties which ban the stockpiling of chemical weapons, but it signed the Geneva conventions that forbid using them in warfare. Syria has tried to avoid confirming whether it possesses poison gas, while denying it has used it.Western countries believe Syria has a vast undeclared arsenal of chemical arms. Sending inspectors to destroy it would be difficult even in peacetime and extraordinarily complicated in the midst of a war.The two main precedents are ominous: U.N. inspectors dismantled the chemical arsenal of Iraqi leader Saddam Hussein in the 1990s but left enough doubt that suspicion he still had such weapons was the basis for a U.S.-led invasion in 2003.Libyan leader Muammar Gaddafi was rehabilitated by the West after agreeing to give up his banned weapons, only to be overthrown with NATO help in 2011.Assad's government says the chemical attack was the work of rebels trying to win Western military support, a scenario that Washington and its allies say is not credible.Human Rights Watch, the New York-based watchdog, said evidence strongly suggested Syrian government forces were behind the attack. It said in a report that the type of rockets and launchers used in the attacks suggested weapon systems in the possession only of government forces.