The U.S. has not presented concrete proof, and U.N. inspectors currently in Syria to investigate alleged chemical attacks have not endorsed the allegations.
After the ambassadors met for a couple of hours at U.N. headquarters, the draft resolution was being sent back to their governments for consultations, according to a Western diplomat, who spoke on condition of anonymity because the discussions were private.
The diplomat said Russia reiterated its objections to international intervention in the Syrian crisis.
U.S. Ambassador Samantha Power and British Ambassador Mark Lyall Grant left the meeting without commenting to reporters.
A spokesman for British Prime Minister David Cameron said in London that the British draft resolution would authorize "all necessary measures under Chapter 7 of the U.N. Charter to protect civilians from chemical weapons."
Chapter 7 allows the use of international armed force to back up U.N. decisions.
Speaking Wednesday from The Hague, Secretary General Ban Ki-moon said no action should be taken until the U.N. chemical weapons inspectors finish their work.
"Let them conclude ... their work for four days and then we will have to analyze scientifically" their findings and send a report to the Security Council, he said.
The U.N. said the analysis would be done "as quickly as possible."
Ban also pleaded for more time to give diplomacy another chance to end the more than two-year conflict that has killed more than 100,000 people.
But the secretary-general added that the Security Council must not go "missing in action."