Snap vote likely
Kostunica said it was likely that a snap election would be held on May 11, the date already set for local elections in Serbia.
The government will function in a reduced capacity until the elections are held, he said.
Kosovo, a predominantly ethnic Albanian province, had been under UN control since 1999, when Nato launched air raids to stop a Serb crackdown on ethnic Albanian separatists.
But Serbia, which considers Kosovo its historic and religious heartland, has dismissed the territory's secession as illegal under international law.
Kostunica has hinted that some of his coalition partners gave up on defending Serbia's claim to Kosovo in favour of better ties with the West, which backed the territory's secession.
Kostunica's stand has found himself in direct conflict with elements within the government, including Boris Tadic, Serbia's president.
The cabinet, made up of Kostunica's conservatives, Tadic's Democratic Party and the G17 Plus party, was formed in May, after months of strained negotiations in the wake of the last parliamentary elections in January 2007.
Tim Judah, an expert on the Balkan's, told Al Jazeera: "There has been a definite crisis in the government since February 17 when Kosovo declared independence."
He said that fresh elections would decide "Serbia's fate" and whether the country "moves towards Europe and the European Union, or goes back into isolation arguing that the fate of Kosovo and the return of Kosovo to Serbia is more important".
Serbia's Tanjug state news agency quoted Kostunica on Friday as saying he "no longer trusts his coalition partners to be sincerely fighting to preserve Kosovo".
Tadic disputed Kostunica's claim that their clash was over Kosovo.
|Kosovo's ethnic Albanian majority declared|
independence from Serbia last month [EPA]
"Kosovo is of course an integral part of our country," Tadic said.
"I believe the issue is that the Serbian government does not have a united position over European and economic perspectives of Serbia and its citizens."
Kostunica's DSS says it will support a resolution in parliament, calling on the EU to "clearly and unambiguously" confirm Serbia's territorial integrity, as a condition for further European integration.
The Democratic Party opposed the resolution in cabinet earlier this week and, with support from the G17 Plus party, defeated the plan two to one.
Those who support EU membership say the resolution would not bring back Kosovo and only serve to halt Serbia's plans to join the EU.