The incoming coalition parties, aiming to form a government by early December, have so far ruled out mandatory jabs and said there will be no new lockdowns -- at least not for the vaccinated.
If the talks are ultimately successful, Social Democrat Olaf Scholz — the finance minister and vice chancellor in the outgoing government — will become Germany's new leader.
Sunday's parliamentary election left Germany's traditional big parties effectively needing the support of the third- and fourth-placed parties.
There are majorities for three more or less plausible new coalition governments, and it could take weeks or months to put a new administration in place.
The Greens made significant gains to finish 3rd but fell far short of their original aim of taking the chancellery, while the Free Democrats improved slightly on a good result from 2017.
The Social Democrats' candidate Olaf Scholz said that the outcome was 'a very clear mandate to ensure now that we put together a good, pragmatic government for Germany'.
Angela Merkel's successor, Armin Laschet, had low personal approval ratings and some in the party had questioned whether he was the right candidate for chancellorship.
Angela Merkel decided not to run for a fifth term and the election campaign has largely focused on the three candidates hoping to succeed her.
The Third Way has incited controversy with divisive public campaigns in the run up to national elections in Germany on September 26.
A crowded race to succeed Chancellor Angela Merkel after she decided not to extend her 16 years in office has left many Germans uninspired and undecided.
The party rattled Germany's political establishment four years ago, when it came third in parliamentary elections after stoking anti-migrant sentiment.
Chancellor Angela Merkel's decision to not seek another term set up the first election since West Germany's inaugural vote, in 1949, in which there is no incumbent seeking re-election.
Armin Laschet, the chancellor candidate from Merkel's center-right Union bloc, insisted that he was 'not at all' frustrated by a poll following Sunday night's debate.