Serbian President Boris Tadic has said he will call an early general election after the coalition government fell apart over policy on Kosovo.
Kosovo Serbs continued to hold anti-independence rallies this week
Prime Minister Vojislav Kostunica announced the collapse after failing to get his cabinet to reject closer EU ties in protest at independence.
Mr Kostunica has said recognition of Kosovo by EU states is illegal.
Mr Tadic is awaiting a formal request for the new election, expected on Monday, before setting a date.
"I respect the prime minister's decision that he is no longer able to lead the government of Serbia and, when I get the government's decision, I will call an election," he said in a statement.
"Elections are the democratic way to overcome political crises and the people are the only ones who have right to decide which is the way forward for Serbia."
The political establishment in Serbia has been deeply divided over the way forward and a general election would be the first opportunity for the people of Serbia to express their views, says the BBC's Nick Hawton in Belgrade.
Kosovo's declaration of independence came nearly a decade after Nato forces expelled Serbian forces from the mainly ethnic-Albanian territory.
Kosovo declared its independence from Serbia on 17 February.
The US and major EU countries have recognised it as independent.
Serbia, backed by its ally, Russia, says it will never accept an independent Kosovo.
Announcing that his cabinet had fallen, Prime Minister Kostunica told reporters in Belgrade:
"The government of Serbia has no united policy any more on an important issue related to the future of the country - Kosovo as a part of Serbia.
"Such a government could not function any more. This is the end of the government and we should return the mandate to the people."
However, Mr Tadic, who says Belgrade will only be able to defend its right to Kosovo if it joins the EU, said the main difference between himself and his prime minister was not on Kosovo but Serbia's "European and economic outlook".
Mr Kostunica's Democratic Party of Serbia (DSS) split with its coalition partner, the Democratic Party (DS) of Mr Tadic, over policy towards the EU in the wake of Kosovo's independence declaration.
The outgoing prime minister has maintained that ties can improve only if the EU rejects Kosovo's declaration of independence.
Belgrade has reacted angrily to an EU mission to ease Kosovo's transition.
The DSS is backing a draft resolution from the opposition nationalist Radical Party, condemning the EU's 1,800-strong mission to Kosovo as illegal and calling on countries to overturn their decision to recognise it.
But a number of pro-Western ministers have failed to support Mr Kostunica's approach.
Mr Kostunica has scheduled a cabinet meeting on Monday to propose an early election for 11 May - the date for Serbia's local elections.