Far-right activists and left-wing counter-protesters have violently clashed in eastern Germany after a man was allegedly killed by two migrants.
German police and security officials are facing criticism over the violence that left at least 20 people injured.
"What we have seen is something which has no place in a constitutional democracy," Angela Merkel said.
Right wing protesters gesture towards police in riot gear as they gather at the place where a man was stabbed. Source: AAP
"We have video recordings of (people) hunting down others, of unruly assemblies, and hate on the streets, and that has nothing to do with our constitutional state."
The protest late on Monday, sparked by the killing of a 35-year-old German man in an altercation with migrants over the weekend, erupted into clashes between neo-Nazis and left-wing counter-protesters.
The German news agency dpa reported that Chemnitz police acknowledged having mobilised too few officers for the demonstration.
Two police officers, nine far-right protesters and nine left-wing counter-protesters were injured in the clashes, dpa reported.
Footage showed officers struggling to prevent far-right protesters breaking through police lines.
The protesters also performed Nazi salutes and chanted "the national resistance is marching here!"
The eastern state of Saxony, where Chemnitz is located, has long been a hotbed of anti-migrant sentiment.
Right wing protesters light flares while facing police. Source: AAP
The far-right Alternative for Germany party received almost a quarter of the vote in Chemnitz last year.
The opposition Green party accused Germany's interior minister, Horst Seehofer, of fanning anti-migrant sentiment in recent months and urged him to think about resigning in the wake of the violence.
Foreign Minister Heiko Maas expressed concern that Germany's reputation could suffer as a result of violent far-right protests.
"We have to keep in mind that these are pictures that will be seen abroad," Maas told reporters in Berlin.
"But I don't think that what was seen there even comes close to reflecting the reality in Germany.
"I firmly believe that the majority of people living in this country want an open and tolerant country."
Maas said it was up to authorities to investigate the killing and hold those responsible to account.
Green lawmaker Konstantin von Notz told the news portal t-online.de that the violence in Chemnitz recalled events in other parts of eastern Germany during the early 1990s, when authorities failed to stop far-right mobs from attacking migrants.
Chemnitz police said they have arrested a 22-year-old Syrian and a 21-year-old Iraqi on suspicion of manslaughter in the death of the German man after a street festival early on Sunday.
Prosecutor Christine Muecke said the killing was preceded by a verbal confrontation that escalated.
