It calls for military action against what Britain has termed Syria’s “unacceptable” use of chemical weapons.
But Russia has said the UN must finish its investigation into the claims before discussing any resolution.
Syria has accused the West of “inventing” excuses to launch a strike.
“Western countries, starting with the United States, are inventing fake scenarios and fictitious alibis to intervene militarily in Syria,” Prime Minister Wael al-Halqi said on Syrian state television.
British Foreign Secretary William Hague told reporters the international community had a responsibility to take action against the Syrian government, even if agreement could not be reached at the UN.
The Syrian government has strongly denied that it used chemical weapons and blames opposition fighters for the attack on 21 August, which reportedly killed hundreds of people near Damascus.
A team of UN weapons inspectors is currently investigating the sites of the attack. UN General Secretary Ban Ki-moon said the experts were expected to finish their investigation in four days and would need more time after that to analyse their findings.
Mr Ban appealed for the team to be given “time to do its job”.
‘Give peace a chance’
Britain’s National Security Council had “unanimously” backed action against Syria over its “unacceptable” chemical weapons use, Prime Minister David Cameron said earlier on Wednesday.
He had gathered the UK’s armed forces and security chiefs with key cabinet ministers for emergency talks over possible military action, ahead of UN Security Council meeting.
The British prime minister said: “We’ve always said we want the UN Security Council to live up to its responsibilities on Syria. Today they have an opportunity to do that.”
The draft resolution would condemn the “chemical weapons attack by [Syria’s President] Assad”, Mr Cameron added.
Mr Ban earlier called on the council’s permanent members – China, Russia, France, the US and the UK – to act together.
“The body interested with maintaining international peace and security cannot be ‘missing in action’,” Mr Ban said.
“The council must at last find the unity to act. It must use its authority for peace,” he went on.
He added: “Give peace a chance. Give diplomacy a chance. Stop fighting and… start talking.”
Meanwhile, in a briefing to journalists, joint UN-Arab League envoy to Syria Lakhdar Brahimi said: “It does seem clear that some kind of substance was used… that killed a lot of people” on 21 August.
But he also emphasized that any military action would need Security Council authorization.
Russia and China have previously vetoed resolutions critical of Syria and may block any text deemed to approve military action.
Russian Foreign Minister Sergei Lavrov warned that “attempts at a military solution will lead only to the further destabilisation” in Syria and the region.
Iran’s Supreme Leader Ayatollah Ali Khamenei warned on Wednesday that US intervention would be a “disaster” for the region.
“The region is like a gunpowder store and the future cannot be predicted,” Mr Khamenei said, according to Iran’s Isna news agency.
Meanwhile the Israeli government has authorized a limited call-up of reserve soldiers. Officials told the BBC that although the likelihood of Israel being drawn into fighting with Syria was very low, the country nevertheless had to prepare for that scenario.
Stocks have fallen on global markets and oil prices have shot up amid growing concern about an impending attack on Syria.
The UN weapons inspectors resumed investigations after having called off work on Tuesday because of security concerns.
On Monday, the team’s convoy was shot at by unidentified snipers. One of their cars came under fire as it crossed the buffer zone between government and rebel-controlled areas.
More than 100,000 people are estimated to have died since the conflict erupted in Syria in March 2011.