BERLIN, Monday, Sept. 19 - After a bitterly fought campaign that many people in this country had believed only a few days ago would produce a historic vote for change, the German electorate failed Sunday to give any party or candidate a clear majority.

Indeed, the vote produced the unusual spectacle in Germany of both main candidates, the incumbent Gerhard Schröder and the challenger Angela Merkel, claiming a mandate to govern as chancellor.

The results gave the right-of-center Christian Democratic Union, led by Mrs. Merkel, the highest vote total, about 35.2 percent. But even an unexpectedly strong showing by her party's main coalition partner, the pro-business Free Democratic Party, failed to give an absolute majority in Parliament to Mrs. Merkel, who had seemed confidently on her way to becoming the first woman to lead Germany just a few weeks ago. Parliament chooses the chancellor.

The Social Democratic Party of Mr. Schröder received 34.3 percent, which means that it has lost the slender majority in Parliament it has long enjoyed with its partner, the Greens, which has enabled Mr. Schröder to govern for seven years.

In that sense, the one sure result is that the present governing coalition has been voted out. But it was also clear that Mr. Schröder, written off by the German media as a political has-been in recent weeks, had engineered a masterful maneuver against Mrs. Merkel.

The election concluded a seesaw campaign in which Mrs. Merkel, 51, who embraced American-style economics and closer ties with the United States, lost her momentum in the final days to Mr. Schröder, 61, a veteran politician who has argued that her economic ideas are unfair.

The election has been widely seen as a crucial one in Germany, the powerhouse of Europe's economy, because it confronted the German public with some very fundamental choices at a time of deep economic difficulty, no growth, high deficits and record unemployment. In essence, Mrs. Merkel, who has often been likened to Margaret Thatcher, campaigned for deep free-market reforms and reductions in social welfare, while Mr. Schröder campaigned on the notion that his government has already put into place the more modest reforms needed.

Given the deeply divided vote, the next few days and weeks will almost surely be taken up by intense negotiations among this country's political parties as they seek to forge a coalition that will give one of the candidates the parliamentary majority needed to become chancellor.

Mrs. Merkel in particular was expected to seek an alliance with her rivals, Mr. Schröder's Social Democrats, creating what has come to be called a "grand coalition," even though Mrs. Merkel spoke out strongly against such a possibility during the campaign.

"Red-Green has lost the election," Mrs. Merkel said in a statement late Sunday. Red-Green is the shorthand commonly used for the Social Democratic/Green Party coalition that has governed since 1998. "That's the good news," Mrs. Merkel added.

"Now we have to form a government," Mrs. Merkel continued, even while admitting, "We would have wished to achieve a better result."

Volker Kauder, the Christian Democratic general secretary, said, "We will first talk to the F.D.P. and then to all the other parties, except the Linkspartei/P.D.S.," referring to a new leftist party that got 8.7 percent of the vote. "We are looking for all possible options to bring about a solution," Mr. Kauder said.

Mr. Schröder fired back, "I don't understand, and I am certain the people in Germany also don't understand, how the conservatives can claim a mandate to lead."

Mr. Schröder argued that his stronger-than-expected showing indicated that the German public wanted him to stay in power as chancellor, and he ruled out cooperating with the conservatives in any "grand coalition" unless he remained chancellor. German law requires that the newly elected Parliament sit within 30 days. Its first order of business will be to elect a parliamentary president, and its second, the chancellor.

Normally, the chancellor is the leader of the party that garnered the most votes, but German election results have rarely given any party an absolute majority on its own, and this has led to what has until now been a stable coalition arrangement - the Social Democrats with the Greens and the Christian Democrats with the Free Democrats.

But Mrs. Merkel's failure to win an absolute majority with the Free Democrats has introduced an almost unprecedented uncertainty into Germany's political system. At the same time, in ruling out any coalition with the Christian Democrats in which he is not chancellor, Mr. Schröder clearly threw up a major, perhaps insurmountable obstacle to the solution that has been most discussed here recently: a coalition of Christian Democrats and Social Democrats with Mrs. Merkel as chancellor.

"I feel I have a mandate to ensure that in the next four years there will be a stable government in our country under my leadership," he said at the Social Democrat headquarters, after Mrs. Merkel spoke at hers.

"Those who wanted a change in the chancellory have failed grandiosely," Mr. Schröder said.

But with the combined Green/Social Democrat vote less than 44 percent of the total, it was unclear how Mr. Schröder thought he could get a majority in the Parliament.

One possibility was that Mr. Schröder would attempt to lure the Free Democrats, who got a surprisingly high 9.8 percent of the vote, to drop their alliance with the Christian Democrats and join with the Social-Democrats and the Greens.

This would have the effect of keeping Mr. Schröder in power, but it would bring into the same government an extremely unlikely ideological combination of Germany's most free-market, antitax party, the Free Democrats, with the traditional leftists of the Social Democrats..

Guido Westerwelle, the Free Democrat chairman, indicated in a statement on Sunday night that his party would not agree to a coalition with Mr. Schröder.

Another possibility is that the new Linkspartei, an odd combination of defectors from the Social Democrats and former East German Communists, would join forces with Mr. Schröder and the Greens, but Mr. Schröder emphatically ruled out that idea during the campaign and in his statement on Sunday he said he was willing to talk to all parties, except the Linkspartei.

"Schröder is playing a real tough power game now," said Claus Leggewie, a political scientist at Giessen University. "His argument is, " 'I have a won a plebiscite of the German people,' but it's unreal because he has no majority."

Still, if the options for Mr. Schröder all seemed fraught with potential difficulty, those for Mrs. Merkel seemed equally tough. Only a few weeks ago, as the election campaign accelerated, polls showed Mrs. Merkel almost a sure winner, in combination with the Free Democrats, so much so that she was treated in the German press almost as if she had already become Germany's first woman chancellor.

Mrs. Merkel seemed to have every advantage given Germany's actual situation - especially an unemployment rate of more than 11 percent that Mr. Schröder, despite many promises, had conspicuously failed to reduce. This failure was the reason for several embarrassing losses in state elections during the fall for the Social Democrats. Indeed it was one such loss, in North Rhine Westphalia in the spring, that led Mr. Schröder to call for early elections, a gesture that at the time was widely interpreted as a way for Mr. Schröder to engineer an early departure from German politics.

But Mrs. Merkel, who campaigned on what she called the need for a thoroughgoing reform to revitalize the German economy, led what many analysts, and, apparently, the German public, felt to be a weak, unfocused and even self-contradictory campaign. Mr. Schröder, meanwhile, made speech after speech hammering at the point that Mrs. Merkel's proposed reforms would mean new inequality in Germany, as well as an end to Germany's traditional social welfare system.

"In my perspective, the majority of the German population is still not ready to accept a real hard reform course," said Uwe Andersen , a political scientist at Ruhr University in Bochum.