Boris Tadic, Serbia's president, was quoted as saying the new talks "open a possibility to reach a compromise solution acceptable for both sides".
The envoys are expected to report to Ban Ki-moon, the UN secretary general, on the progress of the talks before December 10.
Ethnic Albanians, who make up more than 90 per cent of Kosovo's population of 1.8 million, generally want independence.
They favour the adoption of a plan proposed by Martti Ahtisaari, the UN envoy whose suggestions are backed by the US and many Western countries.
Serbia, supported by Russia which wields a veto in the UN Security Council, has rejected Ahtisaari's plan.
Vuk Jeremic, the Serbian foreign minister, who also met the international envoys on Friday, said Belgrade was ready to give Kosovo "the widest possible autonomy in the world," but warned that Kosovo Albanians should also give up some of their independence demands.
Agim Ceku, Kosovo's prime minister, though, warned that the new talks would be "the last delay of the Kosovo status".
"This is an unnecessary delay ... We are firm not to move from our positions," he said on Friday.
Washington and the EU believe Ahtisaari's plan should be the basis for new talks while Moscow says the UN envoy's proposal is not "set in stone".