Britain plans to present a draft resolution later on Wednesday.
But unlike the case of Libya, the draft does not suggest military action against Damascus or sanctions.
In Syria, residents of the northern town of Jisr al-Shughour are said to be fleeing ahead of an expected military assault, after the government said 120 security forces personnel had been killed there.
Residents still in the town have set up checkpoints to monitor any security operations, witnesses say.
The government has warned it will act "with force" to combat "armed gangs" that it blames for the recent killings.
In a separate development, Syria's ambassador to France has denied reports in the French media that she had resigned.
Appearing on French TV, Lamia Chakkour said a telephone interview in which she was reported to have quit was part of a campaign of misinformation against the government of Syrian President Bashar al-Assad.
Revised draft On Tuesday, a British spokesman at the UN said the draft resolution to the 15-member Security Council was expected to be presented on Wednesday afternoon.
Earlier, Alain Juppe said that the repression in Syria was "getting worse" and that "the massacres are on the rise".
"It is inconceivable that the United Nations remains silent on such a matter. We are working with our UK friends to have as large a majority as possible on the Security Council," the French minister added after a council meeting.
However, some council members - like Brazil, South Africa and India - are afraid that the resolution could be the first step towards a Libya-style intervention, the BBC's Barbara Plett at the UN reports.
So Britain and France have revised the text to take in their concerns, diplomats say.
The idea is to build enough support in the council to make it politically difficult for Russian and China - two heavyweights who oppose any action on Syria - to veto the resolution, our correspondent says.
However, a senior Russian diplomat reiterated Moscow's opposition to the proposed resolution.
Speaking in Brussels, Russia's envoy to the EU, Vladimir Chizhov, said: "The prospect of a UN Security Council resolution that's along the same lines as Resolution 1973 on
Libya will not be supported by my country. The use of force, as Libya shows, does not provide answers."