Egypt, New Zealand and Spain presented the measure.
If the US text - seen by Reuters - is put to a vote, diplomats say it would likely be vetoed by key Syrian ally Russian Federation.
The World Health Organization said about 500 patients showed signs of exposure to toxic chemicals following the Douma attack.
U.S. President Donald Trump on Wednesday warned of imminent military action in Syria over a suspected poison gas attack near Damascus that Syrian opposition activists and first responders say killed more than 40 people.
"From what we hear now, I am afraid they are looking for a military option, which is very, very unsafe", Russia's UN Ambassador Vassily Nebenzia told reporters following an emergency council meeting.
Russian Federation on Tuesday vetoed a U.S. -drafted U.N. Security Council resolution that would have created a new inquiry to ascertain blame for chemical weapons attacks in Syria, Reuters reported. The draft received five votes in favor (Russia, China, Ethiopia, Kazakhstan and Bolivia), four votes against (the U.S., the UK, France and Poland) and six abstentions, falling short of the minimum nine votes required for adoption.
But the Syrian moves could limit the damage the United States and its allies might be able to inflict on Syrian President Bashar al-Assad's military.
Asked whether such military action against Syria requires Security Council authorization, Skoog said: "The (UN) Charter is very clear about military intervention".
"The United States...is being run by a neocon (neoconservative) faction that is identical to the kind of ideology which ran the [former US President George] Bush regime", he added.
If the USA text, which was seen by Reuters, is put to a vote, diplomats said it would likely be vetoed by Syrian ally Russian Federation.
"Armed force under mendacious pretext against Syria, where, at the request of the legitimate government of a country, Russian troops have been deployed, could lead to grave repercussions", Nebenzia said.
Washington bombed a Syrian government air base past year over a toxic gas attack. It blamed Islamic State militants for mustard gas use.
The key difference between the two drafts is that the U.S. one would mandate an inquiry to lay blame for chemical weapons attacks in Syria, while the Russian draft would require investigators to report to the Security Council, which would then attribute responsibility.
Nebenzia told the council Tuesday the USA resolution was trying to recreate the JIM, which he said "became a puppet in the hands of anti-Damascus forces".
December 2016: A resolution that calls for a truce in Aleppo is vetoed by both China and Russian Federation. USA officials have been consulting with France, Britain and other allies on a possible joint military operation, but the timing remained in doubt Wednesday.
"We stress the imperative need to preserve evidence, and call upon all relevant authorities to ensure no party tampers with suspected sites, objects, witnesses, or victims before independent monitors and investigators are able to access the area", it said.
Nebenzia said two groups of OPCW experts could be on the ground "as early as this week".