At separate talks in Vienna last week, Serbians and Kosovar Albanians, together with representatives from the diplomatic troika comprising the United States, the European Union and Russia, failed to reach a breakthrough on the status of the breakaway province.
"Only the UN Security Council has the mandate to pass a resolution on the province's future status. Also, it should not be forgotten that under the Serbian Constitution, Kosovo is an integral part of Serbia," Kostunica said during talks with EU envoy Wolfgang Ischinger, who is in Belgrade on a two-day visit.
Kosovo has been a UN protectorate since NATO's 78-day bombing campaign against the former Yugoslavia ended a conflict between Serb forces and Muslim Albanian separatists in 1999. The province has been striving for independence from Serbia ever since.
The Serbian prime minister earlier said all measures had to be taken to prevent Kosovo from proclaiming its independence unilaterally, as such a move would set a dangerous precedent, and seriously undermine the authority of the UN.
In August the diplomatic troika launched a 120-day effort to end the stalemate over Kosovo. The troika has to find a compromise by December 10 between Kosovo's demands for independence and Serbia's rejection of Kosovars' bid for secession, and its offer for "essential autonomy."
Moscow, a traditional ally of Belgrade, has consistently blocked plans for Kosovo's independence, using its UN Security Council veto.