The United Nations Security Council is debating whether Kosovo is ready for talks about its final status.
UN Secretary General Kofi Annan has said the talks should begin despite numerous shortcomings.
Kosovo's ethnic Albanian majority wants independence, but Serbia wants to maintain sovereignty over the province.
Kosovo has been administered by the UN since Nato-led troops expelled Serb forces in 1999 to end the war there.
The head of the UN administration in Kosovo, Soren Jessen-Petersen, told the BBC the current situation was unsustainable.
Serbian Prime Minister Vojislav Kostunica is expected to tell the Security Council that Kosovo should remain part of Serbia despite obtaining wide autonomy.
"Any imposed solution that would seize part of our territory would be a violation of international law," he was quoted as saying before leaving for New York.
Mr Jessen-Petersen told the BBC the two positions are "diametrically opposed", and that asking the two sides to sit down and solve it would "almost be an exercise in futility".
But he was confident that with the help of a UN special envoy, who will shuttle between Pristina and Belgrade and other capitals in the region, an agreement would be reached within a year.
He went on to say that negotiations would be based on a set of principles that have already been agreed.
# no partition of Kosovo
# no return of the situation before March 1999
# no union of Kosovo with neighbouring states
# protection of minorities.
In 1999, Nato launched a 78-day air campaign against Serbia to stop a violent crackdown against ethnic Albanian separatist rebels.
Serbian forces were driven out, and the UN took over the administration of Kosovo, which formally remained a province of Serbia and Montenegro.