Berlin (AFP) - Germany's top-selling Bild daily Tuesday documented racist vitriol against migrants posted by Facebook users in a double-page newspaper spread, as pressure grows on the social network to eliminate hate speech.

A day after thousands of anti-Muslim PEGIDA protesters and anti-fascist counter-demonstrators rallied in the eastern city of Dresden, Bild published dozens of anti-migrant rants under the headline "The Pillory of Shame".

Facebook "agitators" posted xenophobic and threatening comments, which Bild urged the prosecutor general to investigate.

Tensions have grown as Germany has opened its doors to an unprecedented wave of people fleeing war and misery, with arrivals expected to reach one million this year, an influx that has seen Chancellor Angela Merkel's poll ratings slip.

As Germany has seen increasingly angry street protests, attacks on asylum shelters and a knife attack against a pro-refugee politician last Saturday, lawmakers have warned that inflammatory speech can spur violence.

Justice Minister Heiko Maas warned last month that Facebook must not "become a funfair for the far right" and stressed that the US company must delete posts that violate German laws against incitement of racial hatred or violence.

Critics have charged that Facebook cracks down harder on nudity and sexual content than on hate-mongering.

On Monday, prosecutors in the northern city of Hamburg said they were investigating a complaint against three Facebook managers alleging that they failed to act against racist comments posted by users.

Lawyer Chan-jo Jun, who filed the complaint, told news site Spiegel Online that he had flagged more than 60 offending entries to Facebook Germany and claimed it "encourages the dissemination of offensive, punishable content through its actions".

Facebook representatives in mid-September met Maas and pledged to combat racist hate speech, encourage "counter-speech" and step up monitoring of anti-foreigner commentary from some of its 27 million users in Germany.