However, a vote on the draft text presented by the Western trio could be held as early as Thursday, diplomats said.
Russia rejected the draft resolution as “categorically unacceptable,” suggesting it is ready to veto the measure if no compromise text is agreed.
British Ambassador Matthew Rycroft told reporters that “the negotiations continue with our colleagues on the Security Council and I would not anticipate them coming to a conclusion today.”
The draft resolution backs a probe by the Organization of the Prohibition of Chemical Weapons (OPCW) and demands that the Syrian government cooperate to provide information about its military operations on the day of the assault.
At least 72 people, including 20 children, died in Tuesday s attack on a rebel-held town in Idlib province.
Dozens more were left gasping for air, convulsing and foaming at the mouth, doctors said.
It is thought to be the worst chemical weapons attack in Syria since 2013, when sarin gas was used.
Britain, France and the United States blame President Bashar al-Assad s forces for the attack, but the Syrian army has denied any involvement.
“We very much hope that it will be possible for everyone to come together,” Rycroft said. “If not, we will press ahead.”
Russia turned up at the negotiations with a rival draft resolution that made no reference to specific demands that Damascus cooperate with an inquiry, diplomats said.
However, French Ambassador Francois Delattre told reporters that negotiations were being held “in a good spirit” and that “there is a chance” for agreement.
“It s time for action — no doubt about it,” he added.
But other diplomats sounded more pessimistic, saying a Russian veto appeared likely. “It s not going well,” a council diplomat said.
The talks on the proposed council measure opened after US Ambassador Nikki Haley warned of unilateral US action if the United Nations fails to respond to the attack.
“When the United Nations consistently fails in its duty to act collectively, there are times in the life of states that we are compelled to take our own action,” she told an emergency council meeting on the attack on Khan Sheikhun.