Formed in May, the government has lurched from crisis to crisis with Kostunica's party hardening its anti-Western rhetoric and going outside the coalition to seek support in parliament from hard-line nationalists.
Kosovo's decision to break away has fed tensions, with most Serbs deeply opposed to losing a territory they consider to be a historic heartland.
President Boris Tadic must now disband the parliament and set a date for the election, probably on May 11.
Tadic, also the head of the Democrats, said on Sunday that attempts to divide Serbs into patriots and traitors over Kosovo would backfire at the polls.
A strong and stable Serbia would be in a better position to defend its interests, he added.
"If we join the EU, then we can make sure that this outlaw state never becomes an EU member," he said on a TV talk-show.
Dimitrij Rupel, the Slovenian foreign minister, whose country holds the EU's rotating presidency, said he hoped for a victory for pro-European parties in the poll.
"To be quite frank, I don't think there is any other possibility for our Serbian friends than the European Union. Where should they go?" he told reporters on Monday, ahead of talks with his EU counterparts in Brussels.
Rupel said he had seen some "encouraging signs" in that direction, including opinion poll results, and protests by students and intellectuals.
"We have a good opportunity for the people of Serbia to choose their way forward," Javier Solana, the EU foreign policy chief, Said.
"I hope very much they will continue to push for a relationship deep and solid with the EU," he said.
"It's an opportunity for Serbia to choose a European course more firmly than they've done so far," Carl Bildt, the Swedish foreign minister and a respected negotiator in the Balkans during the wars of the 1990s, said.