The US draft text received 11 votes in favor, while Russian Federation and Bolivia voted against it and China and Egypt abstained. "We don't know whether we can come to an agreement".
Turkish, Russian and Iranian foreign ministers will meet in Turkey's Mediterranean city of Antalya at the weekend ahead of a trilateral meeting on Syria in Russia's Sochi city next Wednesday, Turkish foreign minister has said.
Turkey earlier this month said Russian Federation had chose to postpone a planned Syria peace conference with all parties after Ankara objected to the potential inclusion of Kurdish forces.
The 15-nation council was due to vote on Thursday on rival US and Russian bids to renew the worldwide inquiry, diplomats said on Wednesday, a move that could trigger Russia's 10th veto to block action on Syria.
The mandate for the joint inquiry by the United Nations and the Organization for the Prohibition of Chemical Weapons (OPCW), which found the Syrian government used the banned nerve agent sarin in an April 4 attack, expires at midnight Thursday.
A resolution needs nine votes in favor and no vetoes by the United States, France, Russia, Britain or China to be adopted.
While Russia agreed to the 2015 creation of the inquiry, known as the Joint Investigative Mechanism (JIM), it has consistently questioned its findings, which also concluded that the Syrian government used chlorine as a weapon several times.
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Russian Federation and Iran back President Bashar al-Assad in the conflict, while Turkey and the United States support differing rebel groups fighting the government.
He also said that the inquiry fails "basic standards" of an investigation and ignores any information that would cast doubt on Damascus's involvement in the April incident.
French Ambassador Francois Delattre urged council members to "please think twice before throwing it away, because this would be a major setback for the fundamentals of our common security".
"Not doing so would only give consent to such atrocities while tragically failing the Syrian people who have suffered from these despicable acts", it said.
It remains to be seen whether the rival drafts can be reconciled and a way found to continue the JIM's work.
"It's absolutely crucial for the mandate to be renewed", Matthew Rycroft, the United Kingdom ambassador to the UN, told reporters Wednesday.
"What is at stake is the professional, independent, objective, scientific, nonpartisan, depoliticized JIM which we've now got, which we've had before, and which we need in the future", Rycroft said. "The only victor would be the people who want to use chemical weapons in Syria - Assad and the Islamic State".