Martin Schulz, the passionately pro-EU SPD leader, vowed not to enter a grand coalition with Angela Merkel's CDU/CSU bloc in the immediate aftermath of the Bundestag election, which took place last September, but performed a U-turn - under pressure from senior party members and Germany's president Frank-Walter Steinmeier - after Mrs Merkel's efforts to form a three-way coalition with the pro-business Free Democrats and the Green party failed in November. His authority had been eroded after reneging on an earlier promise not to take part in a new coalition with Mrs Merkel.
Andrea Nahles also said she would fight for the ruling coalition with the conservatives of Angela Merkel.
Analysts said Mr Kühnert, who said he has been inspired by the campaign of Bernie Sanders in the USA, did not yet have enough sway over the rump membership of the party to win the vote on the coalition.
Schulz said an extraordinary party congress would be held in the western city of Wiesbaden on April 22 to pick a new leader.
"I depart this office without bitterness or resentment", he said, nearly a year after he was elected as SPD party head with 100 percent of the vote.
Nahles, a plain-speaking 47-year-old former labour minister with a left-wing slant and strong oratory skills, is the frontrunner and would become the first female leader in the party's 154-year history. German media cited a letter by Lange to the SPD leadership in which she called on the party to open itself up to a truly democratic debate over its future orientation.
Schulz's own plans were becoming a major distraction for the SPD.
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. "I am surprised that Andrea Nahles wants to take over the leadership immediately, if only in the interim", Harald Baumann-Hasske, Chairman of the Working Group Social Democratic Lawyers, told the newspaper "Welt".
On Tuesday, Schulz said he hoped his decision to resign would result in party members focusing on the coalition treaty rather than personnel issues. "We need to act now".
The authority of Mrs Merkel, Europe's most dominant figure of the 21st century, has waned following her party's poor showing at last year's national elections which saw a spike in support for nationalists who opposed her migration policies. Ms Merkel's CDU secured five ministries, with the CSU winning a further three.
Malu Dreyer, regional prime minister of Rhineland-Palatinate, said: "The SPD can not remain leaderless".