German Chancellor Angela Merkel's party has suffered its worst-ever result in regional elections in the city-state of Hamburg, exit polls suggest.
Kramp-Karrenbauer's decision to give up her ambition of succeeding Merkel came after an eastern branch of the CDU defied the national party and voted with the far-right Alternative for Germany (AfD) to install a state premier from a third party.
While the SPD defended its position as the strongest force, they shed more than eight points since the 2015 polls.
The vote comes days after a racist gunman killed nine people in shisha bars in the western city of Hanau.
Despite coming in second, the Green party appear to be the biggest victor of the state election, surging more than 13 percentage points since the 2015 ballot to gather over a quarter of the votes, according to projections from pollster infratest dimap.
With the Greens on the rise and CDU and SPD support eroding, Hamburg's results reflect the broader political picture of fragmentation visible in Germany-wide polls.
"The CDU is bigger than either one of us, this is about the future of our country and the CDU", said Spahn, adding it was time to build bridges after past differences with Laschet.
The armed suspect, a 43-year-old German man, fatally shot nine people in the Frankfurt suburb on Wednesday before apparently killing his mother and himself.
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Laschet said despite Germany's low unemployment rate and current prosperity, there is growing concern over rising rents, climate change, migration, digitalization and other issues, and a rise in "hate and anger" against many groups, including increasing anti-Semitism.
Members of the German Greens party, including co-leader Annalena Baerbock and local candidate Katharina Fegebank, react to Hamburg election result. "The Greens have been doing very well across the board in this country and the success this evening has to be seen as part of that process".
The Green party surged in Hamburg state election on Sunday to claim the second place while the far-right Alternative for Germany (AfD) could lose all their seats.
The party is now represented in all 16 German state legislatures and in some parts of the country polls in double digits.
The conservative CDU is suffering a leadership crisis after party leader Annegret Kramp-Karrenbauer announced her resignation earlier this month.
The breach of a historic political taboo provoked a nationwide backlash against both mainstream right-of-centre parties.
It is unclear if she will be able to remain chancellor until then with a new party leader although Kramp-Karrenbauer has said the party expects the new party chair to work alongside the chancellor.