Serbia and Kosovo's prime ministers have clashed at the UN Security Council over the future of Kosovo, displaying bitter divisions between the two rivals.

Serbia's prime minister Ivica Dacic said his country "will never, under any circumstances, implicitly or explicitly, recognise the unilateral declaration of independence by Kosovo's ethnic Albanian authorities".

Kosovo's prime minister Hashim Thaci countered that Kosovo is a state recognised by nearly half the UN's 193 members and its territorial integrity "will never be put into question".

Kosovo came under UN and Nato administration after a 1999 Nato-led air war halted former Yugoslav leader Slobodan Milosevic's crackdown on ethnic Albanian separatists in Kosovo.

But the Security Council resolution that established the interim UN administration left Kosovo's final status in question.

Kosovo's predominantly ethnic Albanian leadership declared independence from Serbia in February 2008, with backing from the US and major EU nations.

But Serbia, supported by Russia, insists Kosovo is legally bound by the Security Council resolution and that the UN still retains authority in Kosovo, although many responsibilities have been transferred to the EU.