A politician in the far-right Alternative for Germany (AfD) party, known for its anti-Muslim rhetoric, has resigned from its board and converted to Islam, the party said on Wednesday.

An AfD election poster - one of several which played on anti-Islamic fears. Photo: Shutterstock

But while Arthur Wagner quit his AfD leadership post in the eastern state of Brandenburg, he remained a member of the party, which says Islam is incompatible with Germany's constitution and wants a ban on minarets and the face-covering burqa.

The AfD became Germany's third largest party in parliament after last September's general election.

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Earlier this month, an AfD lawmaker caused a furore after accusing police of "appeasing the barbaric, Muslim, rapist hordes of men" by tweeting in Arabic.

The party said it stood for the constitutional right of religious freedom, regardless of Wagner's conversion.

"Mr. Wagner could also choose another religion," Daniel Friese, a spokesman of the party, told Berliner Zeitung, noting that Wagner had resigned from the board two weeks ago.

"Mr. Wagner resigned on January 11 from the state board on his own volition. Only afterwards was it known that he had converted to Islam," Friese told Reuters.

Wagner declined to comment on his conversion. "He does not want to speak with the press. He believes it is a private affair," the party spokesman said.