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Far-right protesters in Chemnitz, one giving the stiff-armed Nazi salute, hoisted a large banner showing bloodied women's faces on Monday, above the words "we're colorful until the blood flows."

The message to the boisterous crowd was clear: this is what migrants will do to you wives, sisters and daughters.

But the women pictured were actually victims of unrelated violent crimes, in other countries.

Meanwhile, on Facebook and Twitter, posts praised the German victim of a fatal stabbing that had happened a day earlier in the same city, claiming he was protecting a woman from migrants who were harassing her.

But officials say the dispute stemmed from a verbal altercation between two groups, and harassment of a woman wasn't part of it.

Within hours of the Sunday killing, rumors were spreading on social media, sparking spontaneous protests in the city and drawing thousands more to the streets the following night, when the banner was held aloft.

While suspected crimes by migrants regularly draw attention in Germany, a country still grappling with an influx of refugees three years ago, the speed with which far-right extremists flocked to Chemnitz caught authorities by surprise.

Anti-migrant sentiment in Saxony, the eastern state where Chemnitz is located, is high, with about a quarter of voters backing the far-right Alternative for Germany party in last year's election.

Evidence suggests many of those who came were inspired by false information and the deliberate misrepresentation of facts.

"There is absolutely no evidence that harassment was a reason for this dispute," a spokeswoman for Chemnitz prosecutors, Ingrid Burghart, told The Associated Press on Wednesday.

Claims that the victim was protecting a woman from harassment spread beyond social media, and were picked up outside Germany — including by Russian news channel NTV.

Two years ago, Russia's foreign minister and the country's state media claimed a 13-year-old girl of Russian origin known as "Lisa" had been abducted and raped in Germany, prompting street protests in Berlin.

German authorities later determined the girl made up the kidnapping story and had run away, and cited the false claims as an example of Russian propaganda aimed at destabilizing the German government.

During Monday's protest in Chemnitz, at least 18 people were injured when far-right extremists clashed with counter-demonstrators as police tried to keep the two sides apart.

The violence was widely condemned by German officials and friends of the 35-year-old victim.

Police admitted being unprepared for the size of the crowds, with neo-Nazi groups from outside Chemnitz swelling the number of far-right protesters to 6,000.

"The mobilization was based on anti-foreigner comment, false information and conspiracy theories," said Michael Kretschmer, the governor of Saxony.

He, too, told reporters that "there is no reason to believe there was a dispute involving the protection of a woman and that this is the reason for the crime."

A 22-year-old Syrian and a 21-year-old Iraqi were arrested on suspicion of manslaughter in connection with the killing.

Far-right groups have called for further protests in the coming days.