German Chancellor Angela Merkel has voiced outrage over the sexual assaults and thefts by male gangs in Cologne on New Year's Eve.
Women have made at least 90 criminal complaints to police about the harassment by gangs at Cologne's main railway station on Thursday night.
The scale of the attacks has shocked Germany, with as many as 1000 drunk and aggressive young men involved.
Witnesses and police said the men were of Arab or North African appearance.
Mrs Merkel called Cologne Mayor Henriette Reker on Tuesday and expressed her "outrage over these disgusting attacks and sexual assaults".
The chancellor said everything must be done "to find the perpetrators as quickly and comprehensively as possible and punish them, regardless of their origin or background".
There is an intense debate in Germany about refugees and migrants, who arrived in the country in record numbers last year. But Mayor Reker urged people not to jump to conclusions about the Cologne assailants.
"It's completely improper... to link a group that appeared to come from North Africa with the refugees," she said, after crisis talks with the police.
Earlier Cologne police chief Wolfgang Albers called it "a completely new dimension of crime".
Women were also targeted in Hamburg and Stuttgart in similar attacks, but on a smaller scale.
In Cologne, at least one woman was raped and many were groped, including a volunteer policewoman.
One man described how his partner and 15-year-old daughter were surrounded by an enormous crowd outside the station and he was unable to help.
"The attackers grabbed her and my partner's breasts and groped them between their legs."
Most of the crimes reported to police were robberies.
A policeman told the city's Express news website that he had detained eight suspects.
"They were all asylum seekers, carrying copies of their residence certificates," he said.
However, there was no official confirmation that asylum seekers had been involved in the violence. Germany' migrant influx triggered marches by the anti-Islam Pegida movement last year.
Police were deployed outside the station because of the crowds on New Year's Eve but failed to spot the many attacks, according to reports.