Both Merkel and Schroeder have laid claim to building Germany's next government after neither party won a clear majority in parliamentary elections Sunday, leaving the country, the world's third-largest economy, in political crisis.
The deadlock means Germany could spend weeks without leadership at a time when it desperately needs clear direction to push through badly needed economic reforms. Germany also wants to maintain its strong leadership role within the European Union, particularly in the wake of the EU's failed constitution effort and on the eve of membership talks with Turkey.
Merkel said Thursday's talks took place "in a constructive atmosphere" but indicated her conservative Christian Democratic Union and its sister party, the Bavaria-only Christian Social Union, would not give ground on the issue of who should be chancellor.
"I laid out that I have the responsibility of building a government," Merkel told reporters after the meeting. "And we made it clear that if we come to coalition talks, this question must be cleared up."
Yet the Social Democrats are holding out with their argument that German voters rejected Merkel as chancellor, awarding her party only 27.8 percent support after months of polling as much as 40 percent.
Coupled with the Christian Social Union, the conservatives reached 35.2 percent, just edging Schroeder's party, which won 34.3 percent.