But this time he must share power with the Democratic Party of Boris Tadic, Serbia's president.
The elephant round would involve Kosovo's premier and president, Mr Kostunica and Serbia's president, Boris Tadic.
Serbia's president, Boris Tadic, wants a presidential election too, but this is being resisted by the prime minister, Vojislav Kostunica.
May 26, 2011: Serbian President Boris Tadic announces the arrest of Mladic.
The ruling Democratic Party of President Boris Tadic hopes candidate status might boost its chances of winning the general election it may call early next year.
Under the leadership of President Boris Tadic, Serbia has in recent years enjoyed a warming of relations with Brussels (the arrest of Mr Karadzic in July 2008 helped).
Serbia's government is bitterly divided between supporters of Mr Kostunica and backers of the president, Boris Tadic, who was conspicuous by his absence from the rally on Thursday.
The new government formed this month by President Boris Tadic has said that it wants to deal with the war crimes issue to remove any future obstacles to European integration.
Yet as kingmaker Mr Dacic dropped his alliance with the Democratic Party of Boris Tadic in favour of the Serbian Progressive Party (SNS) led by Tomislav Nikolic, who defeated Mr Tadic in the presidential election.
Serbia's president, Boris Tadic, has been trying to persuade the Serbian parliament to pass a resolution to condemn and commemorate the murder of up to 8, 000 Bosniaks by Bosnian Serb troops in Srebrenica in 1995.
ECONOMIST: More arrests and court cases revive bad Balkan memories
Although Serbia's president, Boris Tadic, congratulated the Montenegrins on independence (and said he would be in charge of Serbia's armed forces), Mr Kostunica and the nationalists around him appeared barely capable of taking in what had happened.
ECONOMIST: Slovakia and Serbia: A tale of two Slavic states | The
Vinci said it was significant that Karadzic's arrest had come just a few weeks after the appointment of a pro-western coalition government spearheaded by the Democratic Party of Serbian President Boris Tadic and new Prime Minister Mirko Cvetkovic following a narrow victory over nationalists in parliamentary elections in May.
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