German Chancellor Angela Merkel's party and her plans to stay on until 2021 were plunged into disarray, after her heir-apparent gave up her leadership ambitions in a deepening crisis over ties between the centre and far-right.

Annegret Kramp-Karrenbauer, the leader of the centre-right Christian Democratic Union (CDU), opted out barely a year in the post, a period marked by internal battles over whether to cooperate with the anti-immigrant Alternative for Germany (AfD).

She announced that she was standing down as CDU leader and would not seek to be the party's candidate for chancellor in next year's general elections.

AKK, as Kramp-Karrenbauer is popularly known, blamed the "unresolved relationship of parts of the CDU with the (far-right) AfD and (far-left) Left party" for her decision, a party source told AFP.

"This is an unusually serious situation for the CDU," said close Merkel ally and Economy Minister Peter Altmaier.

"This is about our future as a modern people's party of the centre."

While the party has a policy of no cooperation with either far left or far-right at a national level, regional CDU lawmakers last week went rogue and voted with MPs from the AfD to oust a far-left state premier in tiny central Thuringia.

The breach in the political dam towards the AfD in Thuringia prompted Merkel's junior partners in the national government, the Social Democratic Party (SPD), to call urgent talks at the weekend about the partnership's future.

AKK's departure, the most prominent political head to roll after the Thuringia crisis, was "unsettling," SPD board member Michael Roth tweeted.

It remains uncertain "whether decent democrats stand together in the battle for democracy and against nationalism," he added.

With the race to the chancellery wide open again, Sueddeutsche Zeitung said the aftershocks could be huge.

"It's very possible that the chancellor's exit is coming closer," it wrote.

Voting alongside the far right breaches one of the fundamental taboos of post-World War II German politics, the refusal of mainstream parties to work with the extremes.

AKK's attempts to impose rigid no-cooperation discipline from Berlin have foundered especially in Germany's former communist east, where strong showings for the AfD and Left in some states threaten the ability of mainstream parties to form functioning coalition majorities.

Germany's next national elections must take place by autumn next year, although the fractious coalition between the CDU, its Bavarian CSU allies and the centre-left SPD may not hold until then.

By this summer, AKK hopes to have organised a process to find the person to lead the CDU into the next federal campaign.