Germany's Christian Democrats (CDU) say their win in Dresden at the weekend confirms their right to lead a coalition government.
Mrs Merkel has held exploratory coalition talks with Mr Schroeder
The party's general secretary Volker Kauder said the Social Democrats (SPD) "must finally clear the way for a government led by Angela Merkel".
The final result gave the CDU a narrow four-seat lead over the SPD - still not enough to form a majority government.
The parties are holding coalition talks, but cannot agree on a leader.
SPD leader Franz Muentefering insisted the Dresden result would have "no impact" on the negotiations.
The Dresden vote had been postponed because a candidate died during the campaign.
Neither the CDU or SPD secured a working majority in last month's general election.
The CDU and its Bavarian sister party, the Christian Social Union (CSU), now have 226 seats in the new parliament, while the SPD has 222.
1. Christian Democrats/Christian Social Union (CDU/CSU): 226
2. Social Democrats (SPD): 222
3. Free Democrats (FDP): 61
4. Left Party: 54
5. Greens: 51
CDU candidate Andreas Laemmel won the Dresden seat with 37% support, ahead of his SPD rival Marlies Vollkmer, who won 32%.
Both Chancellor Gerhard Schroeder and conservative leader Angela Merkel campaigned in Dresden, staking their claim to lead the next government.
The two parties stayed on-message after the Dresden vote.
"There is a (Bundestag) majority that's to the left of the CDU," said Social Democrat MP Sigmar Gabriel after the vote.
He was referring to the theoretical possibility of the SPD forming a government with the new left party - Die Linke - and the Greens.
"We are not using this possibility. We want to govern with the CDU, but the CDU must give us something in return. We say: Schroeder must stay chancellor."
Mr Muentefering had a similar message. "We are clearly the strongest political force," he said.
However, Mr Muentefering may also have indicated some flexibility regarding who will be the next Chancellor.
"In these talks, the whole constellation of the future government will be discussed," he said, not explicitly ruling out the possibility of a government without Mr Schroeder.
The BBC's Ray Furlong in Berlin says the capital has been buzzing with rumours that Mr Schroeder will abandon his claim to the chancellery, possibly after a meeting of the SPD leadership on Monday.
The Social Democrats have denied this. But even if Mr Schroeder does go, negotiations may take weeks if they succeed at all, our correspondent says.
For many in the SPD, Angela Merkel remains unacceptable. The speculation is that Mr Schroeder wants to force her out of the game as his price for quitting.