WASHINGTON — President Obama will not insist on a United Nations Security Council resolution threatening Syria with military action, senior administration officials said Friday, as American and Russian negotiators meeting in Geneva moved closer to an agreement that would seek to ultimately strip Syria of its chemical weapons.

After a second day of marathon talks in Geneva between Secretary of State John Kerry and Foreign Minister Sergey V. Lavrov of Russia, both sides expressed optimism, while American officials here said they would give the process a couple of weeks to see if it gained traction. But daunting obstacles remain to dismantling Syria’s vast chemical arsenal as negotiators try to defuse a confrontation that has inflamed politics on three continents.

A significant sign of movement at the United Nations came when the Obama administration effectively took force off the table in discussions over the shape of a Security Council resolution governing any deal with Syria. Although Mr. Obama reserved the right to order an American military strike without the United Nations’ backing if Syria reneges on its commitments, senior officials said he understood that Russia would never allow a Security Council resolution authorizing force.

As a strategic matter, that statement simply acknowledged the reality on the Security Council, where Russia wields a veto and has vowed to block any military action against Syria, its ally. But Mr. Obama’s decision to concede the point early in talks underscored his desire to forge a workable diplomatic compromise and avoid a strike that would be deeply unpopular at home. It came just days after France, his strongest supporter on Syria, proposed a resolution that included a threat of military action.