The draft document, seen by Western news agencies, says the delay is needed to allow further talks between Serbs and Kosovo's majority ethnic Albanians on the future of the UN-administered Serbian province.
The draft also "demands that the parties refrain from making any unilateral declarations regarding final status during that period."
The original document would have endorsed internationally supervised independence for Kosovo without any delay.
Alejandro Wolff, the U.S. deputy ambassador to the United Nations, said the new draft would be introduced at a UN Security Council meeting on June 20. No date has been set for a vote.
Russia, a traditional ally of Serbia and a veto-wielding Security Council member, has strongly objected to the original draft.
(compiled from agency reports)