Serbs and ethnic Albanians have failed to resolve the future status of Kosovo at a final round of internationally-brokered talks.
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.