Cologne police chief Wolfgang Albers described the men as looking as if they were from 'the Arab or North African region' and mostly between 18 and 35 years old.
About 90 women have reported being robbed, threatened or sexually molested at New Year celebrations outside Cologne's cathedral by young, mostly drunk, men, police said on Tuesday, in events they have described as 'a new dimension in crime'.
Cologne police chief Wolfgang Albers told a news conference officers described the men as looking as if they were from "the Arab or North African region" and mostly between 18 and 35 years old. "We have one complaint that represents a rape," he added.
Integration commissioner Aydan Ozoguz warned against foreigners and refugees, hundreds of thousands of whom have entered Germany largely from Middle Eastern war zones, being put under "blanket suspicion".
Chancellor Angela Merkel expressed shock over the attacks that police said occurred when about 1,000 men split into gangs as officers cleared a square to stop fireworks being thrown from the top of steps into the crowd below.
While politicians also urged people not to place refugees under blanket suspicion, the incident fuelled calls from right-wing groups to stop letting in migrants.
Germany took in just over a million last year, far more than any other European country.
Cologne mayor Henriette Reker said it was "unbelievable and intolerable what happened on New Year's Eve" but there was no reason to believe those involved in the attacks were refugees.
Justice Minister Heiko Maas said Germany would not accept the disgusting attacks on women and described them as "a new scale of organised crime".
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.
"Mrs Merkel, is Germany 'colourful and cosmopolitan' enough for you after the wave of crimes and sexual attacks?" tweeted AfD chief Frauke Petry.
Merkel told Reker in a phone call the attacks deserved a tough response.
"Everything must be done to investigate those responsible as quickly and completely as possible and punish them, regardless of where they are from," she said, according to her spokesman.
There are almost daily attacks on refugee shelters.
"Events like that in Cologne foster xenophobia," said Roland Schaefer, head of Germany's association of towns and localities.
After a crisis meeting, Cologne mayor Reker said new steps would be take to avoid a repeat, including increasing police numbers at big events and installing more security cameras.
She stressed that women must feel safe at traditional carnival celebrations next month when the city closes down for five days of drunken street parades and parties.
Reker was stabbed in the neck and seriously hurt in October, just a day before she was elected mayor. Police said that attack appeared to be motivated by her support for refugees.