The province has been a UN protectorate since Nato forced Belgrade-backed troops to withdraw in 1999.
In his address to the New York talks, Vojislav Kostunica, Serbia's prime minister, ruled out independence for Kosovo.
"Everyone should be aware that it is dangerously foolish to believe that a solution can be imposed on Serbia, and that Serbia would ever recognise that on its territory there exists an independent Kosovo state," he was quoted as saying by Serbian news agencies on Friday.
Members of the six-nation contact group for Kosovo - France, Germany, Italy, Russia, Britain and the United States - said they endorsed UN chief Ban Ki-moon's assessment that "the status quo is not sustainable."
"It has damaging consequences for Kosovo's political, social and economic development and for the underlying stability of the region," a statement released by the contact group on Thursday said.
"A solution therefore has to be found without delay," it continued.
The direct talks are part of a process that begun in August after the UN Security Council failed to agree on UN envoy Martti Ahtisaari's blueprint for Kosovo's supervised independence.
Members of the international troika supervising the talks - Wolfgang Ischinger, EU delegate, Frank Wisner, a US diplomat, and Alexander Botsan-Kharchenko, a Russian envoy - are to report to Ban on the outcome of negotiations by the December deadline.
In an address to the UN General Assembly on Thursday, Tadic called on Kosovo Albanian leaders to compromise.
"We call on the legitimate representatives of Kosovo Albanians to proceed to the resumed negotiations without prejudging the outcome, so that a compromise solution, acceptable to both parties, could be achieved, a solution that would lead to long-term Serbian/Albanian reconciliation," he said.
|Ceku has remained steadfast that Kosovo |
should be independent from Serbia [AP]
Tadic referred to Belgrade's offer to grant Kosovo Albanians "special rights and competences for an autonomous development of their community" within Serbia.
He said a unilateral declaration of independence by Kosovo Albanians would encourage other separatist movements around the world and would have a destabilising effect.
However, Ceku said he remained determined to gain Kosovo's independence.
"We are committed to the independence of Kosovo being defined or decided immediately after December 10," he said.
"We prefer a solution through the Security Council but we are also prepared to offer and make the final solution by ourselves. This process can lead us to making a unilateral declaration of independence," he said.
The US has backed a unilateral declaration of independence while Serbia's ally Russia has blocked a series of Security Council resolutions for Kosovo's "internationally supervised independence."
The issue has also divided the European Union, which is organising a civilian mission in Kosovo despite doubts about the future of the province.