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

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.

Earlier this month, an AfD lawmaker caused a furor 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 spokesperson of the party, told Berliner Zeitung, noting that Wagner had resigned from the board two weeks ago.

"Mr. Wagner resigned on Jan. 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 spokesperson said.