She also said she would stand down as chancellor once the current legislative term ends in 2021.
Crucially, they raise her chance of getting re-elected as party leader at the CDU's convention in December.
A new CDU chair will be elected at the upcoming party conference in December, Deutsche Welle said.
Merkel said she took took responsibility for CDU's poor results in state elections since past year.
She said the SPD would now propose a "discussion paper" in Berlin demanding concrete progress on key issues by next October, including pension rights and better childcare, before deciding whether to remain in the coalition.
The 64-year-old chancellor's personal popularity remains solid but she appeared keen to launch an orderly transition period amid signs that her authority is eroding.
During that momentous upheaval, Merkel, who holds a doctorate in quantum chemistry and was working in a lab, joined a pro-democracy group that would merge with the Christian Democrats of chancellor Helmut Kohl.
Fresh jitters in the German political scenario emerged after Chancellor Merkel's party won the regional poll in the Hesse state despite a large drop in voters' support, showing that the weakness around the CDU party remains largely unabated. Her fourth-term government took office only in March but has become notorious for squabbling.
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Gillum vacationed at a luxury resort in Costa Rica in May 2016 with Corey, as well as another investor in the Edison. Gillum says he didn't understand that he was accepting a "gift" that could be prohibited under the law.
The CDU's general secretary, Annegret Kramp-Karrenbauer, said the coalition needs to identify "three concrete projects for the coming months that we implement".
Merkel has led her conservative Christian Democratic Union since 2000 and Germany since 2005. Merkel's party managed an unimpressive win in Hesse, narrowly salvaging a majority for its regional governing coalition with the Greens in the state.
The arrival of more than a million asylum seekers since has not only left a deep chasm in German society, it has also empowered a far-right party that has upended German politics.
Volker Bouffier's likely re-election as state premier could make the CDU's overall losses less painful and may somewhat improve Ms. Merkel's political future after a turbulent year that inspired many to write her political obituary.
"This would have been unthinkable in 2013, when she nearly won an outright majority in the Federal elections", he added.
In Hesse, where Merkel's CDU rule with the ecologist Greens, the two biggest winners were the Greens and the far-right Alternative for Germany.
Just two weeks earlier, Merkel's conservative CSU sister party suffered a similar drubbing in Bavaria.
She told party top brass her mandate running to 2021 will be "her last term", a party source told AFP, adding that she has no plans to seek a post in the European Commission following that, despite speculation to that effect in Brussels.
The AfD party has representatives in all 16 states in Germany.