Serbs and ethnic Albanians have failed to resolve the future status of Kosovo at a final round of internationally-brokered talks.
Kosovo's Albanian leaders want nothing less than independence
The UN had set a 10 December deadline for a negotiated settlement on Kosovo.
The province's ethnic Albanians demand independence from Serbia but Belgrade has consistently rejected this.
Although both sides say they will avoid a return to violence, the US envoy to Kosovo has warned the "peace of the Balkans is very much at stake".
"It is a volatile region," Frank Wisner said. "We're going into a very difficult time."
"The status quo over Kosovo is not sustainable," he added.
Kosovo's ethnic Albanian leaders have said they would consider a unilateral declaration of independence if the 10 December deadline lapsed without a negotiated deal.
But the EU has cautioned against this, saying Kosovo must only achieve statehood in partnership with international bodies.
Speaking after the final round of talks in Vienna on Wednesday, Kosovo's ethnic Albanian President Fatmir Sejdiu said independence for Kosovo "will happen very quickly" but refused to give an exact date.
However, Serbian President Boris Tadic said Belgrade would "annul" any unilateral declaration of independence by Kosovo.
He said his country would use all legal and diplomatic means to resist such a declaration, stopping short of violence.
Though technically part of Serbia, Kosovo has been administered by the UN for the last eight years.
Belgrade's security forces were driven out of Kosovo by a Nato invasion in 1999, after being accused of the repression of the majority ethnic-Albanian population.
Thousands of international peacekeepers have been deployed in the province to prevent a return to violence.
Russia has supported Serbia's stance at the UN Security Council, arguing that independence for Kosovo could provide dangerous inspiration for separatists elsewhere.
All attempts to decide the final status of Kosovo through negotiations have so far failed.