German state interior minister Ralf Jaeger has said migrants were almost exclusively responsible for the attacks on women in Cologne on New Year's Eve.
More than 100 women reported being threatened, robbed or molested during the city's celebrations.
The minister's comments come amid reports a group of Pakistanis and a Syrian were violently attacked by about 20 unknown assailants on Sunday in the city.
Police made a number of arrests during clashes with protesters in Cologne on Saturday.
Supporters of anti-immigration right-wing movement Pegida have been taking part in a demonstration following mass assaults on women on New Year's Eve, with some throwing firecrackers and beer bottles at police, Reuters reported.
Two people were injured during the protest, with a police spokesman saying some of the protesters came from the "hooligan scene".
More than 3,000 people attended the rally, with police using a water cannon against protesters at one point.
The German Chancellor wants increased powers to block foreigners from being granted asylum if they have any sort of criminal record.
Around 400 people gathered in Cologne to demonstrate against violence against women following a wave of assaults on New Year's Eve.
Authorities in Cologne are holding crisis talks on Tuesday after a string of sexual assaults by large gangs of men.