Daniel Fried, Assistant Secretary for European and Eurasian Affairs, said Kosovo delegates and Rice would consider holding elections either before or after the province's status had been determined.
UN sources said earlier that the United States, France and Britain had drafted a new resolution on Kosovo, which does not automatically grant the Serbian province independence after 120 days of multilateral negotiations.
UN missions are already discussing another, third draft resolution, which has yet to be submitted to the UN Security Council. The third version could provide for additional negotiations between Belgrade and Pristina.
Kosovars, who have been under a UN protectorate since the end of NATO's 78-day bombing campaign in 1999, are seeking independence from Serbia and warning that they may have to take the situation into their own hands if no decision is made soon.