Russian President Vladimir Putin has said any decision on Kosovo's fate must be agreed by Belgrade and Pristina.
Serbia's leader said independence would be resisted peacefully
His UN envoy earlier said that world bodies would not recognise Kosovo if it declared unilateral independence.
The Serb province's ethnic Albanians are set to declare independence with conditional US and EU backing, despite opposition from Belgrade and Moscow.
Talks on Kosovo's future, brokered by the EU, US and Russia, ended last year without agreement.
Kosovo has been run by the UN since 1999, when a US-led Nato bombing campaign drove out Serb forces accused of a brutal crackdown on ethnic Albanian separatism.
Ethnic Albanians now form about 90% of the province's population.
"Any resolution on Kosovo must be approved by both sides," Mr Putin argued in an article published in the Bulgarian press to coincide with his visit to the country.
"It is also clear that any resolution on Kosovo will set a precedent in international practice," Mr Putin said.
Russia has previously warned that a unilateral declaration of independence by Kosovo could set a dangerous precedent for separatist struggles elsewhere in the former Soviet Union.
Kosovo Prime Minister Hashim Thaci told the UN Security Council on Wednesday that independence was necessary for "regional success".
Mr Thaci, whose Democratic Party emerged out of the Kosovo Liberation Army rebel group, said a declaration of independence was only a matter of time.
Moscow meanwhile said Kosovo would never be accepted as a state by the United Nations or other world political bodies if it declared independence.
Its UN envoy was backing Serbian President Boris Tadic who reiterated to the UN Security Council that Belgrade would never accept a sovereign Kosovo.
A US envoy said talks had stalled and it was time to take a decision.
As a permanent veto-wielding member of the 15-nation Security Council, Russia has the power to block any request by Kosovo to join the UN.
Most Kosovo Albanians see no future as part of Serbia
"[Kosovo Albanians] would not become members of the United Nations, they would not become members of international political institutions ... if they go down the road of unilateral declarations," Russian envoy Vitaly Churkin told reporters in New York.
Serbia's president told the Security Council his country would never recognise Kosovo's independence and would "preserve its territorial integrity and sovereignty by all democratic means, legal arguments and diplomacy".
"Serbia will not resort to violence and war," he added, urging a "compromise acceptable to both sides".
Mr Tadic said unilateral recognition of Kosovo's independence would have "unforeseeable consequences for other regions fraught with problems of ethnic separatism".
He shook hands with Mr Thaci, who afterwards told a reporter:
"We shook hands as the leaders of two independent countries."
US envoy Zalmay Khalilzad said the Security Council had failed to solve the dispute over Kosovo and no longer had any role to play in the determination of its status.
"The ultimate solution obviously for the problem of that region is to integrate into the broader European institutions, particularly the EU," he added.