GENEVA—The U.S. and Russia began efforts to dismantle Syria's chemical arms network, building on an uncertain pledge by President Bashar al-Assad to join the international treaty banning the use and production of such weapons.

But Moscow's ability to control Mr. Assad as the disarmament process moves forward emerged as a major issue Thursday, after the Syrian leader said he would hold up plans to surrender his chemical weapons unless the Obama administration stopped threatening to use military force if Damascus didn't comply....