Sensing a dramatic turn, huge crowds of opposition supporters streamed into the streets of downtown Belgrade late Sunday to await official results. Early Monday, the state election commission suspended the official count for the night without announcing any results.
About 70 percent of eligible voters went to the polls, according to unofficial estimates, and analysts said such a strong showing would favor Mr. Kostunica.
Mr. Kostunica's supporters said they would offer proof that their candidate had won the election. Meanwhile, political parties issued differing figures they said were based on their poll watchers' reports.
"There is no doubt that we overwhelmingly won on all levels," said opposition campaign manager Zoran Djindjic. "Milosevic has to seriously understand the judgment of history, and he shouldn't gamble any longer. He has to recognize the defeat."
Cedomir Jovanovic, spokesman of Mr. Kostunica's Democratic Opposition of Serbia, said that based on returns from 45 percent of 10,000 polling stations, Mr. Kostunica was leading with 57 percent to 33 percent for Mr. Milosevic.
Opposition hopes surged soon after midnight when the Radical Party, headed by key Milosevic ally and ultranationalist Vojislav Seslj, said its members on the election commission were reporting Mr. Kostunica ahead in the ballot count.
Then, just before 1 a.m., the neo-Communist party headed by Mr. Milosevic's wife, Mirjana Markovic, said the Yugoslav president was headed for re-election in the first round of voting.
"According to the latest data, Slobodan Milosevic has won 54.8 percent," said Ivan Markovic, a top official of the Yugoslav United Left party.
Mr. Kostunica had been leading in opinion polls despite a campaign marred by a crackdown against opposition supporters, one-sided coverage by the staunchly pro-Milosevic media and the lack of broad-based foreign monitoring. And some analysts expressed doubts that Mr. Milosevic would accept the results if he lost.
Srdjan Bogosavljevic, a respected pollster, said the preliminary results indicated that Milosevic supporters had failed to rig the vote in his favor but that their failure might not stop him from ignoring the results and claiming he won.
"They cannot steal the elections [through fraud], but they can simply declare victory," Mr. Bogosavljevic said in an interview in Belgrade, capital of both Yugoslavia and its larger republic, Serbia.
Mr. Milosevic, who has ruled Yugoslavia for the last 13 years, called the election nine months early in an effort to prolong his hold on power. While no official figures had been released six hours after the polls closed, opposition leaders said they believed that Mr. Milosevic had badly miscalculated.
The United States and other Western powers have invested much effort and money in trying to unite Serbia's opposition, promote independent media and oust Mr. Milosevic, against whom NATO fought a three-month bombing war last year for control of Kosovo.
The conflicting claims of victory followed accusations of widespread voting irregularities, including the arrest and assault of monitors trying to guard against vote-rigging.
"It is worse then ever," said Marko Blagojevic of the independent Center for Free Elections and Democracy. "I don't think elections like this were ever held anywhere, ever since the Stone Age."
Mr. Milosevic refused to let internationally recognized election-monitoring groups into the country, barred most foreign media and then expelled or arrested more than 20 journalists who were in Serbia to cover the vote.
Belgrade instead invited 250 carefully screened election monitors from 52 countries, who Mr. Milosevic's government said were sufficient to certify the vote as free and fair.
Mr. Blagojevic's group deployed 7,500 of its own monitors at polling stations across the country to catalog violations.
Serbian police arrested two of the monitors in the southern city of Nis, an opposition stronghold, as they tried to photograph a member of Mr. Milosevic's Socialist Party campaigning outside polling stations in violation of election law.
Mr. Milosevic, an indicted war-crimes suspect, took many of the steps that made a free and fair election impossible long before Sunday's vote, the opposition charged.
For months, his police had been closing down independent broadcasters, arresting and harassing opposition activists and using the army and claims of foreign plots to destabilize Yugoslavia in order to stir up what his opponents called a "war psychosis."
The Associated Press and the New York Times News Service contributed to this report.