The draft resolution was sent back to the governments of the five countries for consultations, according to a Western diplomat, who spoke on condition of anonymity because the discussions were private.
The United States, Britain and France have blamed the Assad regime for an alleged deadly chemical weapons attack near Damascus last week.
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. But President Barack Obama said late Wednesday that the U.S. has concluded that the Syrian government was responsible.
The Russian government has condemned the idea of striking against Syria before the inspectors present their findings and have warned that acting without Security Council authorization would be illegal.
The U.S. and its allies have questioned the ability of the U.N. team to conduct a meaningful investigation, saying they have faced too many delays in Syria.
U.S. State Department spokeswoman Marie Harf said Washington expects no progress at the United Nations.
"We heard nothing different from the Russians in today's meeting than we have for months and indeed years about Syria," she said "So we have no reason to believe that efforts at the Security Council would be any different than these previous efforts that have failed."
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.
A U.S. official, who spoke on condition of anonymity because of the sensitivity of the discussions, said the Obama administration tried to discourage the British government from pushing the resolution. The official said Washington believed the effort would be futile because of Russia's opposition and introducing it could lend credibility to the argument that U.N. authorization is required for action against Syria.
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."
Syria's Ambassador to the U.N. Bashar Ja'afari, meanwhile, said he sent a letter to Ban demanding that the U.N. experts extend their investigation to what he described as three chemical weapons attacks against Syrian soldiers in Damascus suburbs.
He said the attacks occurred on Aug. 22, 24, and 25 and that dozens of Syrian soldiers are current being treated for inhaling nerve gases.
He also expressed confidence that the British draft resolution would no nowhere because members of the councils "don't believe the authenticity of the allegations" against Syria, a reference to Russia and China.
Ja'afari reiterated his denial that the Syrian government was behind any of the attacks. "The Syrian government is innocent of these allegations," he said.
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Associated Press writer Matthew Lee in Washington contributed to this report.
