The Russian-brokered agreement calls on Syrian president Bashar al-Assad to account for his chemical stockpile within a week and allow for international inspections by the middle of next year.
But while it was welcomed by Israel, Iran and China yesterday, Obama faced criticism at home from Republicans over the likelihood of the Syrian government complying without threat of force.
Meanwhile, the first Syrian official to comment, Ali Haidar, greeted the deal, saying: "These agreements ... are a victory for Syria, achieved thanks to our Russian friends."
Minister of National Reconciliation Mr Haidar is part of the Syrian government, though not close to Assad.
He said Syria welcomed the terms of the US-Russia deal, adding: "They have prevented a war against Syria by denying a pretext to those who wanted to unleash it."
He also echoed US Secretary of State John Kerry and his Kremlin counterpart, Russian foreign minister Sergei Lavrov, in saying it might help Syrians "sit round one table to settle their internal problems".
But rebels, calling the international focus on poison gas a sideshow, dismissed the suggestion that the arms agreement might herald peace talks and said Assad had stepped up his conventional offensive now that the threat of US air strikes has receded.
Air attacks, shelling and raids on the suburbs of Damascus yesterday backed up predictions from supporters and opponents of Assad alike that he would resume the offensive after a lull in which his troops took up defensive positions in expectation of US strikes.
Foreign Secretary William Hague, who described the deal as a "significant step forward", will fly out to Paris today where he will be briefed by Mr Kerry on the agreement hammered out on Saturday following three days of talks in Geneva.
Mr Kerry responded to widespread scepticism about the plan by insisting that it had "the full ability" to remove all Syria's chemical weapons. Mr Kerry stressed that force remains an option if Assad reneges - and US forces will remain in position.
Although welcoming Saturday's deal, international responses to the accord have also been guarded.
Western governments, wary of Assad and mindful of the frustrating years UN weapons inspectors spent in Iraq, have noted the logistical difficulties in destroying one of the world's largest chemical arsenals in the midst of civil war.
Assad's key sponsor Iran hailed a US retreat from "extremist behaviour" and welcomed its "rationality". China, which like Russia opposes US readiness to use force in other sovereign states, was glad of the renewed role for the UN Security Council, on which Beijing too has a veto.
The Syrian government has formally told the UN it will adhere to a treaty banning chemical weapons.
Israel, worried that US leniency toward Assad may encourage Tehran to develop nuclear arms, said the deal would be judged on results.
Mr Kerry assured Israel the chemical weapons pact would be effective. "We cannot have hollow words in the conduct of international affairs, because that affects all other issues, whether Iran or North Korea or others," Mr Kerry said after talks with Israeli prime minister Benjamin Netanyahu.
Mr Kerry had earlier briefed Mr Netanyahu on what he called "the most far-reaching chemical weapons removal ever".