Ambassadors to the UN Security Council are meeting for a closed session on a draft resolution calling for Syrian president Bashar Assad to step aside.
Council diplomats speaking on condition of anonymity because the talks are private said they hope to get a sense of whether Russia will negotiate on the text.
Russian officials have said they will oppose the resolution if it contains any hint of a military intervention or regime change in Syria, a major ally.
US Secretary of State Hillary Clinton and the foreign ministers of Britain and France joined Arab League officials in a high-level meeting at the UN urging council members to approve the resolution.
Martin Nesirky, the spokesman for UN secretary-general Ban Ki-moon, said Mr Ban hopes the international community, and the Security Council in particular, will respond to the violence in Syria with "a unified voice".
"He's concerned that as time passes more people are being killed," Mr Nesirky said. "The need for action is because of the need to stop the killing."
Amnesty International called on Russia to stop what it said was its "unconscionable" obstruction of UN efforts to help end the bloodshed in Syria. The UN said several weeks ago that at least 5,400 people have been killed in the 10-month-old government crackdown on a civilian uprising.
Russia and China used a double veto in October to block an earlier Security Council resolution condemning the violence in Syria.
"Russia's threats to abort a binding UN Security Council resolution on Syria for the second time are utterly irresponsible," Jose Luis Diaz, Amnesty International's UN representative, said.
"Russia bears a heavy responsibility for allowing the brutal crackdown on legitimate dissent in Syria to continue unchecked," he added.