The leader of Germany's "anti-Islamisation" movement PEGIDA has stepped down after a picture emerged of him sporting a Hitler-style haircut and moustache, along with racist slurs he posted on Facebook.

"Yes, I am stepping down from the board," Lutz Bachmann, 41, was quoted as telling Bild daily in an online report on Wednesday.

Addressing his followers on Facebook, he said: "I sincerely apologise to all citizens who felt attacked by my posts."

"They were thoughtless statements that I would not make today. I am sorry that I have damaged the interests of our movement with them and I am acting accordingly."

A photo of Bachmann looking like Nazi leader Adolf Hitler had surfaced Wednesday, going viral on social media and sparking a storm of protest.

Media reports also said that Bachmann had posted comments on Facebook in the past referring to refugees as "beasts" and "filth".

Dresden's public prosecutor was investigating whether to open a case against him on charges of incitement of hatred.

"Hitler selfie"

PEGIDA spokeswoman Kathrin Oertel welcomed Bachmann's resignation, saying that his "Hitler selfie" had been "satire, which is every citizen's right" but that "sweeping insults against strangers" went too far.

She said Bachmann, who founded PEGIDA -- "Patriotic Europeans Against the Islamisation of the Occident" -- in the eastern city of Dresden in October, had posted the picture in September, before he became prominent.

Bachmann took the photo, which shows him with a small black moustache and hair swept into a side-parting, around the time of the publication of a bestselling satirical audiobook about Hitler entitled "Look Who's Back".

The furore it caused torpedoed PEGIDA's recent efforts at a charm offensive with the media to present a more moderate image.

At their first-ever press conference this week, Bachmann and Oertel had distanced themselves from the neo-Nazis who had joined their rallies and said that most of their supporters were citizens fed up with contemporary politics.

About 5,000 right-wing protesters, meanwhile, again started to mass, this time in another eastern city, Leipzig, separated by riot police from thousands of anti-racist counter-demonstrators.

The showing of PEGIDA's Leipzig spin-off "LEGIDA" was, in the early evening, far below the up to 40,000 organisers had expected -- in part because of a large number of people at almost 20 counter demonstrations.