Angela Merkel said she took “full responsibility” for poor performance.
She said: “As chancellor and leader of the CDU I’m politically responsible for everything, for successes and for failures.
“When people are telling us what they think of how the government was formed and what they think of our work during the first seven months of this parliament… then it is a clear signal that things can’t carry on as they are.
“The time has come to open a new chapter.”
Angela Merkel also made it clear she would not handpick her successor as party leader and would “accept any democratic decision taken by my party”.
However, Annegret Kramp-Karrenbauer would be the obvious choice for Merkel loyalists to replace her. She is currently the party secretary.
Health Minister Jens Spahn, a leading critic of Angela Merkel’s open-door migration policies, has also announced his candidacy.
Friedrich Merz, a former leader of the CDU-CSU parliamentary group and an old rival to Angela Merkel, has thrown his hat into the ring.
Angela Merkel’s CDU plunged 11 percentage points to 27% in October 28 elections in the central state of Hesse, according to preliminary results. This was the CDU’s worst showing in the state since 1966.
The SPD, which is in coalition with the CDU nationally, fell by a similar amount to 19.8%.
The main beneficiaries were the Greens, who paradoxically share power with the CDU in the state and have now drawn level with the SPD, and the far-right AfD, who rose to 13%.
The Hesse vote follows a pattern of losses for the two main parties, with the AfD doing particularly well in eastern states.
Two weeks ago, the CDU’s Bavarian ally, the CSU, lost its absolute majority in the state’s parliament which it has dominated since 1957. Like in Hesse, the SPD also lost badly and the Greens and AfD surged.
While the Greens appear to have benefited from the SPD’s slump in support, it seems clear that the centre-right has lost voters to the AfD.
Part of the reason could be anger at Angela Merkel’s decision to open Germany’s borders to large numbers of refugees, a move which the AfD has vehemently opposed.
With temperatures near freezing, Hanover police used water cannon, batons and pepper spray to clear a path for the 600 delegates.
One protester’s leg was broken after he chained himself to a barricade, while an officer was hit on the hand by a flying bottle.
Ten demonstrators were taken into custody.
A total of five protests were scheduled in Hanover on December 2. Some 6,000 people joined a pro-immigration rally in the city center and another rally called by trade unions was expected to draw thousands later.
When the conference got under way an hour late, Jörg Meuthen hailed delegates for helping the party achieve national success within five years of being founded.
He said the party was attracting support from voters put off by the other parties’ “pathetic childish games” amid an ongoing struggle to form a coalition government.
AfD has veered to the right since its inception as an anti-euro force, promoting anti-immigration and anti-Islam policies in its election campaign.
However, this sharp turn has created tension within its own ranks, with former co-leader Frauke Petry quitting within days of the election.
The delegates confirmed the AfD’s rightward trajectory, backing Alexander Gauland, the leader of the parliamentary party, for the co-leadership.
Alexander Gauland, who has pledged to stop “the invasion of foreigners” into Germany, said he had “allowed my friends to convince me to step in”.
Delegates defeated a motion to install Jörg Meuthen as the AfD’s only president.
They are also due to elect a new executive board to decide the ideological direction of AfD and debate policy motions.