He also said Andrea Nahles, the party's parliamentary leader, would take over as the SPD's chairwoman. The plan to quell internal strife with a fast leadership reshuffle now seems to have had the opposite effect, however, with critics questioning the legal basis for Nahles' elevation to interim leader prior to her formal nomination by the party leadership committee.
Ms Nahles, the 47-year-old former employment minister, remains favourite to succeed Mr Schulz and become the first woman to lead the party but Simone Lang, the relatively unknown mayor of Flensburg, a small city near the Danish border, has announced she will stand and force a vote.
A deal struck last week between Mrs Merkel's conservatives and long-term rivals the Social Democrats (SPD) to end more than four months of political deadlock has been followed by anger and recriminations over the compromises both parties had to make to remain in power. However, SPD members have to vote on the change on 22 April.
Kevin Kuehnert, who leads the SPD's youth wing and is campaigning for members to vote against another tie-up with Merkel, welcomed the decision as he said it would enable the party to focus completely on the members' coalition ballot.
"The SPD can build on it if the membership of the party gives us the mandate to enter government", he said. The party's 464,000 party members will vote in a postal ballot on the deal, with the results expected to be announced on March 2.
Treat women better, Bill and Melinda Gates tell President Trump
It's nice, I guess, that Bill and Melinda Gates make donations through their foundation for health and education. Melinda's parents made sure their children took the social justice teachings of the Catholic Church to heart.
The manner in which Mr Schulz originally anointed Ms Nahles as his successor - without broad consultation - rankled with many in the party and resulted in Mr Scholz being appointed as interim leader.
"If I can contribute to that by resigning, it will have been worth it", he said outside the SPD headquarters.
In a cartoon published on Tuesday, the Sueddeutsche Zeitung daily showed Nahles with a whip riding an SPD snail. Former European Parliament Speaker Schulz has been criticized for deciding to continue his joint governance with Merkel's Christian-Democratic Union. Media have speculated that one option might be Katarina Barley, a former SPD general secretary and family minister, or SPD veteran Thomas Oppermann.
The turmoil in the SPD can only distract from criticism of Merkel from within her own party after she handed the foreign and finance ministries to the SPD to secure the coalition deal. The SPD was at a record low of 16.5 percent, barely ahead of the far-right Alternative for Germany (AfD).
German Foreign Minister Gabriel lashed out at Martin Schulz, saying his party colleague had broken a promise not to serve in Chancellor Angela Merkel's new cabinet.