The Serbian government has urged President Boris Tadic to dissolve parliament and hold an early election.
Mr Kostunica, left, said his cabinet could not agree a united policy
The call follows the collapse of Prime Minister Vojislav Kostunica's governing coalition at the weekend.
Ministers failed to agree on whether to suspend ties with the European Union, in protest at recognition of Kosovan independence by some EU members.
Mr Tadic, whose party is pushing for EU membership, has indicated he will grant the request for a snap election.
The EU's Slovenian presidency said on Monday that it hoped pro-EU parties would win the coming election.
Slovenian Foreign Minister Dimitrij Rupel, whose country holds the rotating EU presidency, said: "I don't think there is any other possibility for our Serbian friends than the European Union."
Most EU countries recognised Kosovo after its unilateral declaration of independence on 17 February.
Serbia - and its ally Russia - say they will never accept it.
Last week, Mr Kostunica, a nationalist, called a special meeting to propose that parliament be dissolved and snap elections called.
At that meeting, on Monday, the government approved the proposal.
"It has been established that the government no longer has united and joint policies," the government said in a statement.
The proposal will now be put forward to President Tadic, who has the formal power to order an early general election.
He is expected to make a formal announcement on Monday or Tuesday.
The fresh ballot, which is likely to be held in May, is seen as a way out of Serbia's deepening political crisis, says the BBC's Helen Fawkes in Belgrade.
Serbia's coalition partners disagree over the best strategy - and whether the central issue is ties with the EU or Kosovo's independence.
Mr Kostunica, who leads the Democratic Party of Serbia (DSS), has said recognition of Kosovo by EU states is illegal.
Serbian sentiment over the loss of Kosovo remains volatile
"All parties want Serbia to join the EU, but the question is how - with or without Kosovo," he said on Saturday.
President Tadic says Belgrade will only be able to defend its right to Kosovo if it joins the EU.
He says the main difference between himself and his prime minister is not on Kosovo but Serbia's "European and economic outlook".
"The vote will be a referendum on Serbia's European perspective - or on its isolation," Defence Minister Dragan Sutanovac, vice-president of Mr Tadic's party, was quoted as saying by AP last week.
Kosovo's declaration of independence came nearly a decade after Nato forces expelled Serbian forces from the majority ethnic Albanian territory.