As in Serbia, the decision to cooperate with the tribunal has caused a rift between reformers and nationalists, and could bring down the Croatian Government.
On Friday, the war crimes tribunal's chief prosecutor, Carla Del Ponte, went to Zagreb to urge Mr Racan to act without delay on sealed indictments for two suspects.
As in Serbia, the decision to cooperate with the tribunal has caused a rift between reformers and nationalists, and could bring down the Croatian Government.
Mr Racan also faces demonstrations from war veterans and nationalists.
"I am afraid of unrest. Every normal person should be, now that the tourist season has started, but I hope it will not come to that," he said.
Disturbances took place when one former commander, General Mirko Norac, was arrested in March.
Emergency session
The decision came late on Saturday after an all-day emergency cabinet session.
Deputy Prime Minister Goran Granic and three other ministers, all members of Mr Racan's key ally, the Social Liberal party, resigned immediately afterwards.
The Social Liberals have 23 members in the 151-seat parliament, with the strongly nationalist HDZ, the former ruling party, holding another 41.
If the Social Liberals decide to oppose the government, Mr Racan's Social Democrats will be in danger of losing the confidence vote.
Investigation
The UN war crimes tribunal served two sealed indictments almost a month ago.
There is speculation that Mr Ademi may be accused of responsibility for the killings of dozens of Croatian Serbs during a separate offensive in central Croatia in 1993.
Tribunal prosecutors have been investigating the killings of hundreds of Croatian Serbs following the Croatian army's 1995 offensive to recapture land seized by Yugoslav-backed rebels during the six-month war of 1991.
Veterans opposed
Croatia could face international isolation and even sanctions if the government fails to hand over the men.
Mr Racan said that his government had "preferred to choose the way of cooperation to that of confrontation," adding that "to turn down the request from The Hague would be to plunge Croatia in to the abysses of the Balkans conflict."
But many in the country consider all Croat fighters to be war heroes.
The largest veterans' association of Croatia's 1991 war has threatened to organise widespread protests against any extraditions.
"There will be no extradition; we will prevent them," said veterans' leader Mirko Condic, whose group attracted over 100,000 people to a February rally against the prosecution of General Norac.