Hundreds of police officers in riot gear flooded the streets but failed to contain far-right activists who performed Nazi salutes and hurled bottles and fireworks, prompting counter-demonstrators to strike back.
Spontaneous protests erupted that night, with a vigilante mob reportedly chasing down and attacking foreigners in revenge for the killing.
It prompted more than 1,000 left-wing activists to turn out and face off against the far-right group during a second night of unrest on Monday.
The anti-fascist demonstrators chanted “Nazis out” and “There’s no right to Nazi propaganda” at a larger group of far-right protesters, who responded with “We are louder, we are more” and “Lying press”.
Authorities have admitted too few officers were deployed to manage the protests after footage showed them struggling to prevent far-right activists breaking through police lines.
“What was seen yesterday in parts of Chemnitz and what was recorded on video has no place in our country,” Mr Seibert told reporters in Berlin.
“People ganging up, chasing people who look different from them or who come from elsewhere ... is something we won’t tolerate,” he added.
“This has no place in our cities, and I can say for the German government that we condemn this in the sharpest possible manner.”
Police have condemned the spreading of “online misinformation, rumours, speculation and outright lies” in relation to the man’s killing, which came during a fight following a street festival.
A 23-year-old Syrian and a 22-year-old Iraqi have been arrested on suspicion of manslaughter.
Prosecutor Christine Muecke said the killing was preceded by a verbal confrontation that escalated into violence and investigations were ongoing.
Football hooligans were involved in organising the first demonstration on Sunday in a park in central Chemnitz, an eastern city where almost a quarter of the voters supported the far-right Alternative for Germany (AfD) party last year.
German media reported that Afghan and Syrian teenagers and a 30-year-old Bulgarian man were among those targeted by the marauding far-right mob. None were seriously hurt.
Videos posted on social media appeared to show far-right protesters threatening and chasing passersby.
Markus Frohnmaier, an AfD MP, appeared to endorse the violence, tweeting: “When the state can no longer protect its citizens, people take to the streets and protect themselves.”
His comments were criticised by Mr Seibert, who said: “There is no place in Germany for vigilantism, for groups that want to spread hatred on the streets, for intolerance and racism.”
Germany’s Central Council of Jews condemned the violence, calling it a “civic duty to stand against the right-mob.”
“It must never again be accepted in Germany that people are attacked because of their statements or their background,” added council president Josef Schuster.
Police have faced criticism for their failure to contain the outbreaks of violence, which led to the cancellation of the three-day festival.
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