Witnesses and police described the group as "mostly young men, between 18 and 35 years of age, mostly from North African and Arab regions", though the assailants haven't been identified, Albers said.
The Mayor of Cologne said today that women should adopt a "code of conduct" to prevent future assault at a crisis meeting following the sexual attack of women by 1000 men on New Year's eve.
Police said the attacks occurred as officers were clearing the crowd from the square for safety concerns because they saw men firing firecrackers into the throngs of celebrants.
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.
The attackers also reportedly threw fireworks into large crowds and tore the underwear off at least one victim.
Germany was shocked over the holiday at the violent crime against women carried about by about 1,000 men, according to police in Cologne.
Around 150 people gathered in front of Cologne's cathedral on Tuesday evening to protest against violence against women.
And German Justice Minister Heiko Maas tweeted that "we won't tolerate these abhorrent assaults on women - all those responsible must be brought to justice".
New Year's attacks have sparked a strong wave of criticism of German handling of the migrant open-door policy introduced by Chancellor Angela Merkel in September that resulted in over a million of refugees intake in Germany.
There are also fears that a number of women did not report assaults.
Cologne's police spokesman Thomas Held told NBC News that authorities had fielded around 90 complaints of pick-pocketing, groping and at least one of rape.
Many women were sexually assaulted on New Year's Eve in the Cologne city center in a series of coordinated attacks.
A police auto passes the central railway station in Cologne, Germany, Tuesday Jan. 5, 2016. "We'll have to do a better job of explaining to people from different cultures living here that a celebratory atmosphere on the streets has nothing at all to do with sexual attacks".
The police Chief Wolfgang Albers in Cologne said no arrests were made.
The right-wing Alternative for Germany (AfD), which has gained in polls in part at Merkel's expense thanks to a campaign against refugees, said she should close the border. They said much of the mugging and molestation took place later, in the early hours of New Year's Day.