Voters in Bavaria have delivered a "painful" blow to Angela Merkel's coalition allies in a regional election observers say threatens to further destabilise her crisis-hit government.

The Christian Social Union (CSU), partners in Ms Merkel's ruling coalition, lost their majority as they mustered just 37.2% of the vote — down more than ten percentage points from 47.7% five years ago, and their worst performance in the state for nearly 70 years.

In addition, her junior coalition partners, the centre-left Social Democrats (SPD), saw their support in the state halved.

"It's going to be turbulent," the Die Welt newspaper said in a banner headline. "The result in Bavaria is a vote against the grand coalition in Berlin."

Liberal-minded voters flocked to the German Green party, which finished second with 17.5% of the vote — double their total in 2013.

The Greens offered voters a more liberal approach to migration in contrast to the CSU, and the party linked environmental conservation to traditional German culture during campaigning.

The far-right Alternative for Germany (AfD) also prospered, entering the state legislature with 10.2% of the vote.

The CSU has governed Bavaria, a prosperous economic powerhouse home to 13 million people, and has previously held an absolute majority in the state parliament for all but five of the past 56 years.

Power struggles in the national government have weighed on the party, which is traditionally more conservative than Ms Merkel's Christian Democratic Union.

The two parties have clashed on migration, after the CSU took a hard line on the issue.

"Of course this isn't an easy day for the CSU," Bavaria's governor, Markus Soeder, told supporters in Munich, adding that the party accepted the "painful" result "with humility".

"It's not so easy to uncouple yourself from the national trend completely," he added, implying that the situation in Berlin had helped to erode the party's support.

Horst Seehofer, the CSU leader who is also Germany's interior minister, has often been involved in internal coalition squabbling in the capital.

Mr Seehofer has clashed repeatedly with Ms Merkel about migration since 2015, when he attacked her decision to leave Germany's borders open as refugees crossed the Balkans.

In June the two leaders argued over whether to turn back small numbers of asylum-seekers at the German-Austrian border, briefly threatening to bring down the national government.

The CSU will now need to form a coalition to govern Bavaria and Mr Soeder said his preference was for a centre-right alliance.

That would see the CSU partner with the Free Voters, a local conservative rival that made modest gains to win 11.6%.

The Greens are traditionally bitter opponents of the CSU, though they too remain a possible coalition partner.

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Polls indicate the CSU and CDU are set for further setbacks in two weeks in an election in the western state of Hesse, where AfD and the Greens are set for further gains.

The state is ruled by Merkel's CDU in coalition with the Greens, and a slump in support for the conservatives there would almost certainly further weaken her authority.