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The German chancellor Angela Merkel has told leaders of her Christian Democrats (CDU) that she will not seek re-election as party chairwoman at a conference in early December, sources have told German media.

Merkel's conservative Christian Democratic Union is defending its 19-year hold on Hesse, previously a stronghold of the center-left Social Democrats, the chancellor's federal coalition partners in Berlin.

After 13 years with Merkel at the helm, a lot of them in coalition with the SPD, many Germans are exhausted of government by carefully-crafted compromise, calling instead for clear direction on pressing policy issues like migration, security, reform of the European Union and climate change.

The clear victor of Sunday's state polls is the Green Party, in another repeat of the recent Bavarian election.

Meanwhile, the Greens - already the junior government partner in Hesse - look poised to nearly double their 2013 vote share to around 20 percent, topping the 17.5 percent they scored in conservative Bavaria.

Alternative für Deutschland (AfD) - 12%.

Chancellor Angela Merkel's junior coalition partners gave her conservatives until next year to deliver more policy results, threatening to end their alliance if there is no improvement after both parties suffered in a regional election on Sunday. Confirming polls' predictions, the far-right party, buoyed by a backlash against the arrival of more than 1 million refugees in Germany after 2015, is poised to enter the Hesse parliament, the last of Germany's 16 state parliaments from which it was absent.

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The result is another milestone in the long decline of the big-tent "people's parties" CDU and SPD that have dominated German politics for decades. The two parties in power in Berlin, the chancellor's Christian Democratic Union and the center-left Social Democrats, lost 11 percentage points each in a high-stakes vote in Hesse on Sunday.

Back in 2013, the CDU had to make a coalition with the Alliance 90/The Greens after the election resulted in no clear victor.

Die Welt reporter Robin Alexander said the path could now be clear for Merkel's chosen heir, CDU general secretary Annegret Kramp-Karrenbauer, to take the reins if no other credible candidate emerges by December.

"We could then gauge the implementation of this roadmap at the agreed mid-term review, when we would be able to clearly see if this government is the right place for us", Nahles told reporters.

Seehofer said Monday that "it's a shame" that Merkel plans to step down as CDU leader, although she intends to remain chancellor.

Standing down now would allow the next party leader to build a profile before the next national election, which is due in 2021. But its share of the vote plummeted to about 27 percent, its poorest result in half a century in the wealthy state and a far cry from the 38 percent it achieved in the last state election just five years ago.