Vitaly Churkin, Russia's UN ambassador, said the crisis in Lebanon was too urgent to wait for the wording of a draft resolution on the withdrawal of Israeli troops and a permanent ceasefire to be agreed.
He said: "This diplomatic activity is not being conducted in a quiet academic environment.
"War is raging in Lebanon and the humanitarian situation is getting catastrophic."
The Russian ambassador said that Kofi Annan, the UN secretary general, supported his proposal that would urge diplomats to speed up their efforts to seek a political solution.
Churkin said: "We hope it will focus minds, it will energize politicians and diplomats."
The United States and France have been leading diplomatic efforts to bring an end to the fighting but have failed so far to reach an agreement on the timetable for Israel to leave southern Lebanon.
John Bolton, the US ambassador, said he did not think it was helpful to distract attention from negotiations over the US-French draft.
"We're not playing games here," he said before adding that he had not given up hope for an agreement on Friday.
John Bolton said he had not given
up hope of agreeing a resolution
There had been encouraging signs for a deal on Thursday when a spokeswoman for Tony Blair, the British prime minister, said "there is the potential for an agreement within 24 hours".
Philippe Douste-Blazy, the French foreign minister, had also been in a positive mood. He said: "Things are moving in New York today [Thursday]. I hope they move even more quickly and in the hours to come."
It had been suggested that the UN would vote on Friday on a resolution calling for an end to hostilities and the gradual pull out of Israeli troops as the Lebanese army, supported by an international peacekeeping force, is deployed in the south.
But the Lebanese foreign minister said that US and French proposals are unsatisfactory because they do not provide an immediate ceasefire.
Fawzi Salloukh told Aljazeera that Lebanon had seen copies of both drafts but "neither draft meets Lebanese aspirations, especially since they concur on not stipulating an immediate ceasefire".
Salloukh also criticised the proposals for being "vague" on the demand that Israel withdraw from the Shebaa Farms region and said there was "discrimination" on the issue of prisoners.
He said that under the proposed drafts, the two Israeli soldiers captured by Hezbollah would have to be freed, but "the issue of the Lebanese prisoners should [merely] be dealt with quickly".
The US is thought to favour a single comprehensive resolution which would authorise the use of force by international peacekeepers while France wanted an initial resolution to end the fighting followed by a second to set up the force.
Earlier, a senior official in Beirut had called the draft resolutions "tangible progress".
Israel said it has put plans to expand the ground offensive in southern Lebanon on hold in order to give diplomacy a chance.