Chancellor Angela Merkel called for a thorough investigation of the "repugnant" attacks, ranging from groping to at least one reported rape, allegedly committed in a large crowd of revellers during year-end festivities outside the city's main train station and its famed Gothic cathedral.
Her spokesman Steffen Seibert said she had called Cologne's mayor, Henriette Reker, to express her "outrage" over the violence, which she said required "a tough response from the state".
Police in Cologne said they had received 90 criminal complaints by today and quoted witnesses as saying that groups of 20-30 young men "who appeared to be of Arab or North African origin" had surrounded victims, assaulted them and in several cases robbed them.
A plain-clothed policewoman was reportedly among those attacked.
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"We assume more people will come forward," police chief Wolfgang Albers told reporters.
The northern port city of Hamburg also reported around 10 similar attacks against women on New Year's Eve.
Asked by a journalist whether refugees were behind the rampage, Maas said police were still working to identify the attackers.
"This is not about where someone is from but what they did," he said.
"Making an issue out of it, lumping it together with the refugee issue, is nothing but exploitation. Now is the time to determine the facts and then decide on the necessary consequences."
Interior Minister Thomas de Maiziere said he was stunned by the "despicable" assaults.