The backing for Merkel came on Tuesday while Schroeder appeared to show greater flexibility by saying all sides should drop any "pre-conditions".
German voters ousted Schroeder's government on Sunday, but did not give Merkel a parliamentary majority, leaving Europe's largest economy - beset by high unemployment, sluggish growth and budget deficits - rudderless.
Both Schroeder and Merkel claim they have a mandate to be the next chancellor, a dispute to be settled in coalition talks beginning on Thursday among Germany's political parties.
But the outcome is far from clear: one could win, or both could conceivably be overlooked by their own parties.
The two parties between them will have enough votes to form a clear majority government, but will have to overcome differences on policy and principles.
Two prominent politicians from the left and right earlier indicated that a "grand coalition" would be the best way out of Germany's political muddle.
They disagreed on Merkel and Schroeder's clashing claims to become chancellor.
Voters ousted Schroeder's ruling coalition of Social Democrats and Greens on Sunday, but withheld a majority from the Christian Democrats and their partners, the pro-business Free Democrats.
The result has been a confused scramble for power.
Voters withheld a majority from
the ruling Red-Green coalition
Social Democratic Interior Minister Otto Schily gave a nod towards a possible left-right government in an interview published on Tuesday in Italy's Corriere della Sera newspaper.
"The needle is oscillating more towards a grand coalition under the leadership of Schroeder," Schily said.
Guenther Beckstein, interior minister in the state of Bavaria and a member of the Christian Social Union (the Christian Democrats sister party), agreed that the coalition was the way forward.
"For me, the given result must be a grand coalition under the leadership of Mrs Merkel," said Beckstein, a candidate for Merkel's cabinet had she won a majority on Sunday.
Another possibility is an all-left coalition between Social Democrats, Greens and the New Left Party, made up of renegade Social Democrats unhappy with Schroeder's pro-business reforms and former East German communists.
Both Schroeder and Left Party leaders have ruled it out, but there remains speculation it could succeed through toleration by the Left Party, which would support it without directly participating by taking cabinet posts.
"The needle is oscillating more towards a grand coalition under the leadership of Schroeder"
Social Democrat Minister
A top labour leader, IG Metall industrial union head Juergen Peters, endorsed Schroeder's bid to remain chancellor after seven years, and expressed support for an all-left government, although conceding it might be unrealistic.
He concluded, however, that "Schroeder's chances aren't bad" to stay in office.