The spate of sexual assaults and muggings prompted protests in Cologne over the weekend that at times turned violent.
Many of the protesters were angry at police response to the attacks as well as the influx of migrants and refugees into Europe.
"Where were you on New Year's Eve?" one protester yelled at police. "Why didn't you protect those women?"
Right-wing groups threw beer bottles, firecrackers and stones at officers in riot gear. Cologne police responded with tear gas and water cannons.
German Chancellor Angela Merkel has condemned the attacks in Germany as "disgusting, criminal acts." But she did not back down on her commitment to welcome refugees who obey German laws and pledge to integrate into German society.
Cologne Police Chief Wolfgang Albers was fired Friday amid criticism of his department's handling of the violence.
And German Justice Minister Heiko Maas was among many who expressed disapproval of Cologne Mayor Henriette Reker for advising women to keep "more than an arm's length" away from unknown men.
Reker later said the comments had been taken out of context.
Other attacks in Europe
Reports of other New Year's Eve attacks have emerged from elsewhere across Europe
Police in Kalmar, Sweden, said Friday they had arrested two men described as refugees. The men, who have since been released on bail, are suspected in two of the 11 sexual harassment complaints received in the town on New Year's Eve, police spokesman Johan Bruun said.
Police are looking for 10 to 15 more suspects who allegedly encircled a group of women in Kalmar and groped them, Bruun told CNN.
In all, 16 females from ages 17 to 21 said they were molested, he said.
In Salzburg, an Austrian city on the German border, two men have been charged with sexually assaulting women on New Year's Eve and New Year's Day, police said in a statement.
A 23-year-old Syrian citizen was arrested in the city's Old Town section on New Year's Eve after sending fireworks in the direction of a 17-year-old student, police said. She was slightly injured in her abdomen. Further investigation revealed the suspect allegedly had sexually abused a 20-year-old from Bayern in the inner city before the fireworks incident, police said.
And in Zurich, Switzerland, six women told authorities they were "robbed from one side, (while) being groped ... on the other side" by groups of men, Zurich police said Friday.
And in Helsinki, Finland, police said they are investigating two possible criminal offenses related to New Year's Eve harassment centered around "a gathering of asylum-seekers."
Both the Zurich and Helsinki allegations became public well after the incidents took place.