Angela Merkel’s Bavarian allies are heading for their worst state election result in more than 60 years in a regional vote likely to increase tensions within Germany’s fragile coalition government.

According to the latest polls, the Christian Social Union (CSU) should win about 34% of the vote, losing the absolute majority with which the centre-right party has controlled its south-eastern heartland for most of the period since the second world war.

Polling stations opened on Sunday with sunny weather likely to increase turnout. Broadcasters are expected to publish exit polls shortly after 6pm (5pm BST).

The pro-immigration Green party is likely to be one of the biggest winners, projected to more than double its share of the vote to up to 19% and overtake the centre-left Social Democrats (SPD) as the second biggest party.

The Free Voters regional protest party and the anti-immigration Alternative for Germany (AfD) are both forecast to win roughly 10% of the vote.

This could complicate the efforts of the CSU state premier, Markus Söder, to form a stable coalition government in Bavaria.

The splintered result could force Söder, who has ruled out a coalition with the AfD, into an awkward alliance with the Greens.

Horst Seehofer, the CSU party leader and interior minister in Merkel’s federal government, could face calls to give up at least one of his posts following the Bavarian election because his hardline rhetoric against asylum seekers is likely to scare away voters.

“We’ve lost trust because of the CSU,” Volker Bouffier, the deputy party leader of Merkel’s Christian Democratic Union (CDU), told the Welt am Sonntag newspaper. He accused Seehofer of damaging the image of the CDU/CSU alliance. Bouffier is state premier in Hesse, where an election will be held later this month.

Seehofer has been among Merkel’s fiercest critics following her decision in 2015 to welcome more than a million asylum seekers. He has gradually shifted the CSU, the sister party to the CDU, to the right to counter the rise of the AfD.

Divisions between the conservative allies have widened in recent months after an inconclusive national election last year forced them into a coalition with the left-leaning SPD. Merkel’s fourth and probably final government has already come close to collapsing twice in arguments over immigration and a scandal over Germany’s former domestic spymaster.

The parties are also at odds over how to phase out polluting diesel cars and whether to grant tax cuts for the rich.

The Bavarian election followed a mass protest in Berlin on Saturday in which more than 200,000 people demonstrated against racism, xenophobia and the rise of the far right.

• This article was amended on 14 October 2018 to correct the picture caption that had referred to Markus Söder as Markus Volker Bouffier.