US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov met for a second day in Geneva to work on Moscow's disarmament proposal; Washington remains sceptical and Kerry has said US military action is still possible to punish Assad for a poison gas attack in rebel territory last month.
However, after meeting the UN envoy for Syria, both Kerry and Lavrov said progress on the arms issue in their talks could help relaunch their efforts to bring Syria's warring sides together and negotiate an end to a conflict that has inflamed the Middle East and divided world powers since it began in 2011.
There is little sign of compromise inside Syria, however, where sectarian and ethnic hatreds have been deepened by two and a half years of war that has killed over 100,000 people and forced up to a third of the population from their homes.
Air strikes and artillery bombardments on rebel-held suburbs of the Syrian capital on Friday followed defiant comments from Assad a day earlier after he agreed, at prompting from his Russian ally, to sign up to a global ban on chemical weapons.
Kerry told a joint news conference: "We are committed to trying to work together, beginning with this initiative on the chemical weapons, in hopes that those efforts could pay off and bring peace and stability to a war-torn part of the world."
He hoped a date might be set for peace talks, but added: "Much ... will depend on the capacity to have success here in the next hours, days, on the subject of the chemical weapons."
Talks with Lavrov, which also involved U.S. and Russian weapons experts, are expected to last until Saturday in Geneva.
After meeting UN envoy Lakhdar Brahimi, Lavrov and Kerry said they hoped to meet in New York in about two weeks, around September 28 during the UN General Assembly, to see if they could schedule a new international peace conference on Syria.
Lavrov, voicing regret at the failure of an international accord reached at Geneva last year, said he hoped a "Geneva 2" meeting could lead to a political settlement for Syria.
"We agreed ... to see where we are and see what the Syrian parties think about it and do about it," he said.
Russia has resisted calls from Syrian rebels and Western and Arab leaders for Assad to make way for an interim transitional government. Russian President Vladimir Putin, warning against what he calls Western interference in sovereign states without UN backing, says outsiders should not impose a settlement.
Assad's Syrian opponents, many of them disheartened by the failure of U.S. President Barack Obama to make good on threats to launch military strikes in response to the August 21 gas attack, say they see no place for Assad after the war.
However, neither side has been able to finish the fighting, leaving the country's territory divided and its people in misery, including two million who are now refugees abroad.
Fighting in Damascus
As the diplomacy continued in Switzerland, Assad's forces were on the offensive around Damascus, opposition activists and residents said. Warplanes and artillery were bombing and shelling, notably in the Barzeh neighbourhood, where activists said there were also clashes on the ground.
"It seems that the government is back to its old routine after the past couple of weeks of taking a defensive posture from a US strike," said one resident of central Damascus, who opposes Assad. She heard jets overhead and artillery in action.
Syria formally applied to join a global poison gas ban - a move welcomed on Friday by Putin. Calling it "an important step" towards resolving the crisis, he said: "This confirms the serious intention of our Syrian partners to follow this path."
China, too, hailed Assad's decision, as did Iran, Assad's key ally in a regional confrontation with sectarian overtones between Shi'ite Tehran and Sunni Muslim Arab states.
But Kerry has underscored that Washington could still attack: "This is not a game," he said on Thursday.
The talks were part of a diplomatic push that prompted Obama to put on hold his plans for US air strikes in response to the chemical weapons attack. Moscow's proposal also spared Obama facing a vote in Congress on military action that he had appeared increasingly likely to lose at this stage.
The United States and its allies say Assad's forces carried out the attack with sarin nerve gas, killing more than 1,400 people. Putin and Assad have blamed rebel forces.
The Syrian opposition complains that chemical weapons are a sideshow and want their allies to step up their support, notably in the form of armaments, in order to help them topple Assad. Rebels say Assad has been buoyed by Obama's failure to attack.
The United Nations said on Thursday it received a document from Syria on joining the global anti-chemical weapons treaty, a move Assad promised as part of a deal to avoid US air strikes.
But the Syrian leader told Russian state television that he would finalise plans to abandon his arsenal only when the United States stopped threatening to attack.
"When we see the United States really wants stability in our region and stops threatening, striving to attack, and also ceases arms deliveries to terrorists, then we will believe that the necessary processes can be finalised," he said on Thursday.
Lavrov said Moscow assumed no US attack would be necessary now, though US officials say only the threat of force has prompted Assad to comply and Kerry said that Washington could yet act if it was not satisfied.
He said any arms agreement must be comprehensive, verifiable, credible and implemented in a "timely" way.
Experts say removing Syria's hundreds of tonnes of chemical weapons, scattered in secret installations, would pose huge technical problems at the best of times, let alone in the middle of a civil war or with authorities which do not fully cooperate.