Shortly after, the party's leadership announced that it supported the chairman of the SPD parliamentary group Andrea Nahles for the post.
Hoping to contain the bitter infighting inside the party, the SPD has nominated Nahles to replace Schulz, pending approval on April 22 at a special party conference in the western city of Wiesbaden.
Nahles, 47, shot to national political fame during the fraught days of the last SPD government 15 years ago when, as a left-wing lawmaker, she helped lead a party rebellion against its tough social reforms.
The move comes ahead of a ballot of the SPD's 464,000 members, who get the chance to veto a coalition deal agreed last week with Chancellor Angela Merkel's conservatives.
The new agreement between the two parties has seen the CDU give the SPD three prestigious ministerial posts of finance, foreign affairs and labour.
Schulz said that he hoped his resignation would pave the way for "a new beginning" of the SPD and allow party members to focus on the coalition deal rather than personnel issues.
Martin Schulz bows out as SPD leader, leaving his party in a mess. "But I think the whole situation is not only bad for the SPD, it's a bad situation for all parties because people lose more and more trust in political parties".
US Senate begins debate on immigration
Just an hour previous, Cornyn had told reporters the opposite, saying: "We could do it this week if there is cooperation". Unfortunately, people covered by DACA were children when they came to the United States but that does not make it legal.
Tensions are also reported between him and Sigmar Gabriel, an SPD colleague who is now foreign minister. A vote against could sweep away the current generation of leaders and trigger new elections, unsettling partners in Europe and beyond.
Among supporters of Merkel's Christian Democrats and their Bavarian sister party, the Christian Social Union (CSU) - with whom the SPD are poised to form a with coalition government - 71.6 percent were critical of the SPD's ability to govern. The far-right populist Alternative for Germany (AfD) entered the Bundestag for the first time.
Merkel annoyed members of her Christian Democrats (CDU) by agreeing in the coalition talks to cede the finance ministry to the SPD.
Martin Schulz formally resigned as leader of Germany's Social Democrats, drawing the curtain on his career in the upper echelon of domestic politics less than a year after he took over the party.
The SPD's turmoil broke into the open again Tuesday over the question of Schulz's successor.
The SPD originally wanted to reinvent itself in opposition but reconsidered when Merkel's attempt to form an alliance with two smaller parties failed late previous year.