The text obtained by AFP states that the Security Council "decides in the event of future non-compliance... to impose measures under chapter 7" of the UN charter, which provides for sanctions and possibly military force.
The draft resolution submitted to the 15 council members "condemns in the strongest terms any use of any toxic chemical, such as chlorine, as a weapon in the Syrian Arab Republic."
The US move at the United Nations followed a report by the OPCW chemical watchdog in January that concluded "with a high degree of confidence" that chlorine gas had been used in attacks on three villages in Syria last year.
At least 13 people died in the attacks that were carried out from April to August, according to the report by the Hague-based Organization for the Prohibition of Chemical Weapons.
While the report did not attribute responsibility for the chlorine attacks, it cited 32 witnesses who saw or heard the sound of helicopters as bombs struck and that 29 smelled chlorine. Only the Syrian regime has helicopters.
President Bashar al-Assad's regime and the rebels have accused each other of using chemical agents, including chlorine, in the nearly four-year war that has killed more than 210,000 people.
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After an August 2013 sarin attack outside Damascus that much of the international community blamed on Assad's government, the regime agreed to turn over its chemical arsenal.
But Syria did not have to declare its stockpile of chlorine -- a toxic agent that can be considered a chemical weapon -- as part of a disarmament deal agreed in 2013 because it is widely used for commercial and domestic purposes.
The US draft resolution stresses that those responsible for the use of chlorine and other toxic chemicals must be held accountable.
Security Council experts were to meet Thursday to discuss the draft resolution, which could come up for a vote on Friday, diplomats said.
It remained unclear whether Russia, Assad's ally, would support the text and its serious threat of punitive measures.
Even if the draft resolution were to be adopted, any concrete action against Damascus would have to be approved by the council, giving Russia an opportunity to block further steps.
On Thursday, the council will also receive a report on progress in ridding Syria of its chemical weapons production sites, in line with the 2013 agreement reached between the United States and Russia.