The leader of a German organisation opposed to perceived "Islamisation" of Europe stepped down after online posts surfaced in which he used derogatory language to refer to refugees and posed looking like Adolf Hitler.

Lutz Bachmann, co-founder of the Patriotic Europeans against the Islamisation of the West, or PEGIDA, announced his departure on Facebook.

It followed German media publishing the comments where he called refugees "cattle" and "filthy," and a photo showing him with a Hitler moustache and hair combed over like the Nazi Fuehrer.

Mr Bachmann did not comment directly on the picture, but apologised for the anti-refugee comments, which he made online in September, a month before the group staged its first protest.

"I earnestly apologise to all citizens, who felt attacked by my postings," he said on the group's Facebook page.

"They were ill-considered comments that I wouldn't make in this way today," he added, expressing regret for harming the movement, which has taken pains to distance itself from neo-Nazi groups.

The group has staged weekly demonstrations in the eastern city of Dresden that reached their peak last week, drawing 25,000 people.

This week's planned rally was cancelled after police said authorities had monitored a Tweet calling for one of the organisers to be killed.

PEGIDA's spokeswoman, Kathrin Oertel, said the Hitler picture had been satire, but Mr Bachmann's comments about refugees and others he made about German politicians had not "contributed to the trustworthiness" of the group.

Bild newspaper quoted Mr Bachmann as saying he had posted the Hitler picture on his Facebook page, apparently some time ago, as a joke.

"One has to be able sometimes to make fun of oneself," he said.

If it was a joke, nobody was laughing.

"Anyone in politics who poses as Hitler is either a total idiot or a Nazi," vice chancellor Sigmar Gabriel told Bild, taking the opportunity to reiterate the government's call for people to stay away from PEGIDA's demonstrations.

A protest staged by a separate group in the eastern city of Leipzig met violent counter-demonstrations yesterday.

Police said some among the 20,000 counter-protesters tried to break through barriers protecting the route where about 15,000 supporters of the group, calling itself LEGIDA, were marching.