Russia's UN ambassador, Vitaly Churkin, is quoted as saying the new draft is "unacceptable" to Moscow.
The new text, drafted by the United States and European Union countries, would give Serbs and ethnic Albanians four more months to try to reach a mutually acceptable agreement on Kosovo's future.
The draft also demands that the "parties refrain from making any unilateral declarations regarding final status during that period."
No date has been set for a vote.
The original document would have endorsed internationally supervised independence for Kosovo without any delay.
Russia, a traditional ally of Serbia and a veto-wielding Security Council member, has strongly objected to the original draft.
(AP, ITAR-TASS)