Angela Merkel on Tuesday night said "hate in the streets" has no place in Germany as she condemned Right-wing anti-immigration vigilante groups attacking foreign migrants.

After the fatal stabbing of a German man, 35, allegedly by a Syrian and an Iraqi, thousands of protesters marched in the eastern city of Chemnitz for two straight days, some chasing down people they believed were immigrants.

Police reported assaults by extremists against at least three foreigners, while investigations were opened in 10 cases of the protesters performing the illegal Hitler salute.

"What we have seen is something which has no place in a constitutional democracy," Mrs Merkel told journalists.

"We have video recordings of (people) hunting down others, of unruly assemblies, and hate in the streets, and that has nothing to do with our constitutional state."

Her comments came as the German interior minister pledged reinforcements for police amid muted calls by some far-Right groups for a third evening of demonstrations on Tuesday.