At least 106 criminal complaints have been filed since last week, Cologne police spokesman Christoph Gilles said.
The figure has increased from 90 since Tuesday.
“At least three-quarters have a sexual component. In two cases, we are investigating crimes that amount to rape,” Mr Gilles said.
About 1,000 men described by police as being of “Arab or North African origin” gathered around Cologne’s main station, next to the city’s famous cathedral, on New Year’s Eve.
Smaller groups surrounded individual women, harassed them and stole their belongings.
Police initially failed to mention the assaults in reports the following morning, describing the festivities as “largely peaceful”.
Details of the attacks only emerged over the weekend and calls have grown for a comprehensive review of police actions on the night, after some witnesses claimed that officers did not stop the attackers.
Mr Gilles said police were well prepared on the night, but “surprised” by the scale and aggression of the attacks.
Mayor Henriette Reker said she expected police to analyse what went wrong and “draw consequences from that”.
Police chief Wolfgang Albers has shrugged off questions about his own future, saying that he will stay in his post, though he acknowledged the initial failure to mention the assaults was a mistake.
Ralf Jaeger, North Rhine-Westphalia state’s interior minister, said he expected a detailed report from Cologne police this week on who knew what when.
Mr Gilles said the city has 10 officers working on the attacks and four men have been detained.
Among the angles police are investigating is whether there are any links to similar crimes committed over the past two years in the nearby city of Dusseldorf, where men have groped women to distract them before stealing their belongings.
The two cities are 25 miles apart.
Markus Niesczeri, a spokesman for Dusseldorf police, said that since the start of 2014, officers there have identified more than 2,000 suspects of North African origin in connection with organised thefts.
He declined to say whether there have been any arrests in those cases.
In addition to widespread shock over the scale and nature of the attacks, the incident has also fuelled public debate about Germany’s ability to integrate large numbers of migrants.
Germany registered nearly 1.1m people as asylum seekers last year.