Churkin said the resolution's chances of adoption were "zero".
"Almost the entire text and maybe particularly the annexes are permeated with the concept of the independence of Kosovo," he said.
Kosovo, where 90 per cent of the two million people are ethnic Albanians, has been run by the UN since 1999, when Nato bombs forced out Serb troops that were killing and expelling Albanians in a two-year war.
Substituting European representatives for the UN would reduce the influence of the Security Council, and by extension Russia, an ally of Serbia.
Jean-Marc de la Sabliere, France's UN ambassador, speaking on behalf of the sponsors, said it was difficult to guess what to do after four months of negotiations should the resolution be adopted.
He said the sponsors would consult with their capitals.
If Kosovo and Serbia reached an agreement, the council could adopt a resolution endorsing it.
If they did not, members would have to review what to do next. "We cannot say today. We do not know," de la Sabliere said.
Ban Ki-moon, the UN secretary-general, expressed concern that Kosovo's leaders would declare unilateral independence from Serbia, even if this deprived them of European aid.
"I would hope that Kosovo will not take any unilateral action," Ban said.
"Any further delay or prolongation in this issue is not desirable, not only for Balkan states, but also for all European countries."
Western diplomats said Russia was not negotiating on the text so they would have to consult with their respective governments on the next step.
On Friday, Zalmay Khalilzad, the US ambassador, threatened to move forwards on Kosovo, which wants independence from Serbia, outside the Security Council whether Russia agreed or not to the resolution.
Khalilzad said if Russia continued to object "this will not stop the situation from moving forward, but it will be outside the Security Council framework, which is not what we want."