Also Friday, former President Jimmy Carter, said "a punitive military response without a U.N. Security Council mandate or broad support from NATO and the Arab League would be illegal under international law and unlikely to alter the course of the war."
Defense Secretary Chuck Hagel has repeatedly said the United States will respond to Syria in concert with allies.
"Our approach is to continue to find an international coalition that will act together," he told journalists Friday in Manila, Philippines.
Skeptics of military action have pointed at the decision to use force in Iraq, when the United States government under Bush marched to war based on a thin claim that dictator Saddam Hussein was harboring weapons of mass destruction.
Opponents are conjuring up a possible repeat of that scenario in Syria, though the intelligence being gathered on the use of WMDs in Syria may be more sound.
An NBC News poll conducted Wednesday and Thursday indicated that 50% of the public says the United States should not take military action against Damascus in response to the Syrian government's alleged use of chemical weapons against its own citizens, with 42% saying military action would be appropriate.
But the survey suggested that if military action would be confined to air strikes using cruise missiles, support rises.
More than 160 legislators, including 63 of Obama's fellow Democrats, signed letters calling for either a vote or at least a "full debate" before any U.S. action.