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'.
The Election Committee will select 40 of 90 lawmakers in the city's legislature during elections in December, as well as elect the Hong Kong leader during polls in March next year.
The race to replace Angela Merkel has boiled down to a competition between Vice-Chancellor Olaf Scholz of the centre-left Social Democrats and Armin Laschet of Merkel's CDU-CSU conservative alliance.
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.
Things started to go wrong for Laschet in mid-July, when deadly floods struck western Germany -- including North Rhine-Westphalia, where he is state premier.