Since Yugoslav President Slobodan Milosevic's ouster last week, there have been behind-the-scenes struggles for control of the police, the courts, the banking system and customs authorities, officials said. Many Serbian authorities remain loyal to Mr. Milosevic.
Mr. Kostunica's 18-party coalition has formed a "crisis committee" that is moving through institutions one by one, trying to ensure support for a new democratic authority, sources said.
On Sunday, officials loyal to Mr. Milosevic sought to block a plan by President Kostunica to consolidate his power by replacing the government of Serbia with a group of experts who would rule until new elections in several months, The Washington Post reported.
The Serbian republic's president is Milan Milutinovic, a Milosevic ally who was indicted last year by the U.N. war crimes tribunal for alleged involvement in atrocities in the Serbian province of Kosovo.
At a private meeting Sunday night with Mr. Kostunica, Mr. Milutinovic refused to accede to Mr. Kostunica's demand that Milosevic loyalists in the Serbian government step down immediately, said an official familiar with the talks.
Mr. Kostunica, who met with top army generals Sunday, has said that securing such a mass resignation is essential to cementing his power at the federal level and interrupting damaging Milosevic policies.
Mr. Milutinovic told Mr. Kostunica that he had to consult with others in the Socialist Party before he could accept such a demand.
"He has been consulting directly with Milosevic," said the official, who asked not to be identified. "We are certain of it."
The Serbian parliament is scheduled to convene Monday for the first time since the elections. Some of Mr. Kostunica's allies called for a new street protest in an effort to force parliament to dissolve.
Zoran Djindjic, who served as Mr. Kostunica's campaign manager, has sought in recent days to block Mr. Milosevic's influence within various government ministries, sources said Sunday. He dispatched paramilitary soldiers to exert control at the headquarters of the Serbian republic police in Belgrade, they said.
On Friday, the still-forming Kostunica government took over the central financial institution, the National Bank of Yugoslavia, in a move that immediately stabilized the free-falling dinar.
Mr. Kostunica's allies also seized the federal Customs Building on Friday and recovered documents they will turn over to prosecutors that implicate government officials in cigarette smuggling, officials said.
"It is very important to control our institutions," said Srboljub Antic, a member of an independent group of economists. "We are afraid that people who are on the top of those institutions could do a lot of harm to prevent or postpone the reforms."
Milan Protic, the mayor-elect of Belgrade and head of the New Serbia party, said Saturday that "the members of the old regime are trying to cover their traces, and trying to destroy all the evidence that might implicate them for all types of things â€“ financial, political and other stuff."
President Clinton called Mr. Kostunica on Sunday to "express the admiration of the American people" for ousting Mr. Milosevic and moving toward democracy, said P.J. Crowley, spokesman for the White House's National Security Council.
Mr. Clinton told Mr. Kostunica that "a lot of hard work" lies ahead in the transition to democracy, and both leaders indicated their desire for "more normal" relations between the countries.
To help shore up Mr. Kostunica's government, the European Union has said in recent days that it plans to donate more than $2 billion in aid to Yugoslavia during the next five years.
EU foreign ministers meeting in Luxembourg are expected to take steps Monday to lift the oil embargo imposed during the Kosovo war in 1999, end the ban on commercial flights to and from Serbia and ease financial restrictions on Serbian firms and people.
Clinton administration officials said Sunday that the United States would support Yugoslavia's re-entry into the United Nations and the end of oil sanctions. But U.S. officials said they would not support Yugoslavia's reintegration into other world institutions until its new government cooperates with the war crimes tribunal, a policy Mr. Kostunica has said he did not support.
Mr. Milosevic and aides have been charged with war crimes in Kosovo that triggered NATO's 78-day bombing campaign last year. They have not been arrested or brought to trial.
Robin Cook, the British foreign secretary, said in London that decisions about Mr. Milosevic's future could wait until the government consolidated its power. But he said that Mr. Kostunica's victory presented "a better chance" of bringing Mr. Milosevic to trial in The Hague.
The Washington Post, New York Times, Knight Ridder Newspapers and Associated Press contributed to this report.