The Saxon member of the Bundestag Sören Pellmann and the MEP Martin Schirdewan have announced their candidacies for the party chairmanship of the left.
Pellmann said in Berlin on Tuesday that he wanted "to take on concrete responsibility for my party in a difficult situation".
Schirdewan had previously confirmed his candidacy.
A new dual leadership is to be elected at a party conference in Erfurt at the end of June.
The currently sole chairperson, Janine Wissler, is running again.
More applications are expected.
Pellmann said at a press conference in Berlin that in future the left would be about “talking more to each other than about each other”.
The member of the Bundestag said about the orientation of the content: "The left stands like no other party for the social question".
As a further focus, he mentioned showing “a clear edge against right-wing extremists”.
Schirdewan said on Tuesday on ARD that it would be "a great honor for him if the party congress elected me party chairman".
The left is in a difficult phase.
He trusts himself to lead the party out of this crisis "in a team that works together in a spirit of trust".
It is about strengthening the profile “again as a modern socialist justice party”.
Referring to the series of electoral defeats, Schirdewan said: "We obviously have a lot of homework to do, that's what the voters told us." What is needed is a "programmatic renewal" of the left.
"For me, this primarily concerns the reconciliation of social and ecological issues."
As a further focus, Schirdewan named the digital change from the perspective of dependent employees and those who cannot afford to participate in technological progress.
The party would also have to redefine foreign and security policy issues.
"And we need a structural renewal that, among other things, also addresses the accusations of sexism that have arisen among us and makes us really recognizable as a feminist party," he added.
Schirdewan is co-chairman of the Left Party in the European Parliament.
The 46-year-old was born in East Berlin, worked as a political scientist and moved into the EU Parliament for the first time in 2017 as a successor.
The 45-year-old Pellmann won the direct mandate in the Leipzig II constituency in the federal elections last September. He has been a member of the Bundestag since 2017.
The elementary school teacher is the Eastern Commissioner for the left-wing parliamentary group and spokesman for inclusion and participation.
In April, Wissler's co-leader Susanne Hennig-Wellsow resigned after only 14 months.
In addition to private motives, she cited the failed renewal of the party and the reports of sexual assaults on the Hessian left as reasons.