Angela Merkel's conservatives won Germany's election by just three seats, falling far short of a majority and leaving the country in political limbo.
Germany now faces days and possibly weeks of uncertainty which could result in the two parties forming a coalition.
Both Mrs Merkel and Mr Schroeder say they have a mandate to be chancellor.
The outcome defies pre-election opinion polls predicting that Mrs Merkel would be the clear winner.
She is unlikely to be able to form her preferred coalition and may have to join with the Mr Schroeder's centre-left SPD in a "grand coalition".
The BBC's William Horsley in Berlin says such a coalition could lead to instability or gridlock as the two sides differ sharply over how to raise Germany's economic spirits.
"We would naturally have wanted a better result," Mrs Merkel said, but she insisted she was still on course to become the country's first woman chancellor, reports BBC.
According to Globe & Mail, Mr. Schroeder, written off as a lame duck a few weeks ago, refused to concede defeat, saying he could still theoretically remain in power if talks with other parties were successful.
"I feel myself confirmed in ensuring on behalf of our country that there is in the next four years a stable government under my leadership," he said to cheering supporters at party headquarters, flashing the thumbs-up signal and holding his arms aloft like a victorious prizefighter.
But Mr. Merkel claimed a mandate from voters to form a new coalition government. Voters were choosing lawmakers for the 598-seat lower house of parliament, which elects the chancellor to head the government.
"What is important now is to form a stable government for the people in Germany, and we ... quite clearly have the mandate to do that," she said.
The result was a big comedown for Ms. Merkel, who smiled but twisted her fingers in apparent agitation as she argued that she had a mandate to be the next chancellor. A grinning Mr. Schroeder said the apparent outcome marked a failure for Ms. Merkel.
Both Ms. Merkel and Mr. Schroeder said they would talk to all parties except the Left Party. Free Democrats leader Guido Westerwelle said his party would not work with the current government pair, the Social Democrats and Greens.
Rescuers found the pilot of one of the two Su-34 fighters that had collided in midair in the Far East on January 18