* Kerry, Lavrov agree to push for new peace conference
* Deal on chemical weapons could help in that process
* Putin welcomes Assad commitment on chemical weapons
* Kerry warns that U.S. could still strike if not satisfied
By Tom Miles and Oliver Holmes
GENEVA/BEIRUT, Sept 13 (Reuters) - Russia and the United States agreed a new push to negotiate an end to Syria's civil war as they discussed a plan to destroy President Bashar al-Assad's chemical weapons in order to avert U.S. air strikes.
U.S. Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov met to work on Moscow's disarmament proposal; Washington remains sceptical and Kerry has said U.S. military action is still possible to punish Assad for a poison gas attack in rebel territory last month.
U.N. Secretary-General Ban Ki-moon said a report by U.N. chemical weapons experts would confirm that poison gas was used in that attack.
"I believe that the report will be an overwhelming, overwhelming report that chemical weapons (were) used even though I cannot publicly say at this time before I receive this report," Ban said at a U.N. meeting in New York.
Ban also said that Assad "has committed many crimes against humanity," though he did not say whether it was Assad's forces or rebels who used chemical toxins in the Aug. 21 attack.
The United States has blamed Assad's government for the attack, while Russia and Assad say it was the work of rebel forces.
On the second day of their talks in Geneva, Kerry and Lavrov said progress on the chemical arms issue 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 U.N. envoy Lakhdar Brahimi, Lavrov and Kerry said they hoped to meet in New York in about two weeks, around Sept. 28 during the U.N. 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 a transitional government.
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 Aug. 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.
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 U.S. strike," said one resident of central Damascus, who opposes Assad. She heard jets overhead and artillery in action.
U.N. investigators said Syrian government forces were bombing and shelling hospitals in rebel areas to stop sick and wounded getting treatment, acts which constituted war crimes.
Fighters loyal to Assad purposefully denied people medical care as a "weapon of war", they said in a report.
The Geneva talks were part of a diplomatic push that prompted Obama to put on hold his plans for U.S. 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.
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 U.S. air strikes.
The Organisation for the Prohibition of Chemical Weapons said on Friday Syria's deputy foreign minister had contacted it with a request for technical assistance.
But Assad told Russian state television that he would finalise plans to abandon his chemical arsenal only when the United States stopped threatening to attack.
Experts say removing Syria's hundreds of tonnes of chemical weapons, scattered in secret installations, would pose huge technical problems in the middle of a civil war.