"That also means that my personal ambitions must come behind the interests of the party".
Mr Schulz, facing criticism inside the SPD, said he did not want debate about his role to jeopardise a new coalition.
Schulz was Merkel's defeated challenger in September.
The Social Democrats are also in disarray after their leader, Martin Schulz, on Friday abandoned plans to become Germany's next foreign minister, saying he hoped the decision would shore up support among SPD members for the coalition deal.
There has been more than four months of coalition negotiations - a German post-war record - since inconclusive elections in September.
Merkel, now serving as acting chancellor, suggested that last week's marathon coalition talks with the Social Democrats were on the brink of collapse over the smaller party's cabinet demands.
Kevin Kuehnert, the head of the SPD's youth wing, made clear on Friday that he remained determined to block a repeat deal with Merkel. "The political carnival in Berlin is far away".
A survey of 5,127 voters conducted by pollster Civey on Wednesday for t-online indicated that nearly 60% of SPD supporters want the party's members to back the coalition deal. But it is unclear whether the party membership will be as open to supporting Merkel.
In an interview with public broadcaster ZDF, Merkel described giving up the Finance Ministry as "painful", but said it would have been "irresponsible" to let coalition talks fail over how to divvy up Cabinet positions.
The names of the CDU politicians who will fill the empty ministry posts will be announced by February 26, when party delegates meet to decide on the coalition deal.
The SPD's 460,000 members will have the final say on the whole agreement in a postal vote, the result of which will be announced on 2 March. There is little chance they will block it, but the gathering will show off just how much Merkel's star has faded among a base that has always been loyal to the hilt, as a growing volume of grumbling has made clear since this week. "The coalition agreement is not the Bible", von Stetten told the German Augsburger Allgemeine newspaper.
Last week, she secured a deal with the SPD to renew a right-left alliance that has ruled Germany since 2013 after making painful concessions on Europe and fiscal policy as well as ceding the finance ministry.
Olaf Scholz, of the Social Democratic Party (SPD) that this week struck a deal to reform Germany's so-called grand coalition government with Chancellor Angela Merkel, said Germany "doesn't need to dictate to other European states how they run themselves". "But her farewell to power has begun, and thereby the debate about her succession", news weekly Der Spiegel commented.