The men suspected of attacking women in Cologne on New Year's Eve were "almost exclusively" from a migration background, mainly North African and Arab, an official report says.
Cologne police also made "serious mistakes" in not calling reinforcements and the way they informed the public.
More than 500 criminal complaints were filed, 40% alleging sexual assault.
Apparent retaliatory attacks in Cologne on Sunday were condemned by the government as inexcusable.
A group of 20 men attacked at least six Pakistani nationals in the German city of Cologne, with two hospitalized for their injuries, police said.
A man of Syrian descent was later attacked and injured by five men.
Two men have been detained following the Sunday attacks, Cologne police said.
Germany is reeling from the mob attacks in the center of the city in western Germany on New Year's Eve. Large numbers of women reported sexual assaults or robberies by gangs of men of Arab or North African appearance.
The number of criminal charges from the episode has risen to 516 -- 40% of which relate to sexual assaults, Cologne police said.
Other European cities experienced similar rashes of sex crime reports from New Year's Eve, with more than 50 similar incidents reported in the northern German city of Hamburg.
Cologne police have said 31 people, most of them North African or Middle Eastern countries, have been charged so far over the attacks. Of those, 18 have been identified as asylum seekers.
The crimes have sparked fierce public debate about the wisdom of German Chancellor Angela Merkel's liberal policies toward migrants, and unleashed a wave of anger toward authorities for their response to the assaults.
Sunday's attacks are the first time anger surrounding the incident has boiled over into reported assaults on minority groups.
On Saturday, protesters from groups opposed to immigration from Muslim countries took to the streets of Cologne, where they were met with left-wing counter-protests.
"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.
Attacks 'coordinated and prepared' ?
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.
In an interview published in Germany's "Bild am Sonntag" newspaper Sunday, Justice Minister Heiko Maas expressed his view that the attacks were not opportunistic, but a premeditated and organized assault on women.
"No one can tell me that it wasn't coordinated and prepared," he told the newspaper. "My suspicion is that this specific date was picked, and a certain number of people expected. This would again add another dimension (to the offending)."
German news organization Spiegel Online reported last week that police kept encountering women and girls in tears on New Year's Eve, citing an internal federal police report.
"Women in company or who were on their own had to run the gauntlet through an inebriated mass of men," the police report read.
Groups of men prevented police from reaching people crying out for help, while the assailants threatened anyone who might try to identify them, the report said.
Cologne Police Chief Wolfgang Albers was fired Friday amid criticism of his department's handling of the violence, while Cologne Mayor Henriette Reker has been slammed for advising women to keep "more than an arm's length" away from unknown men in response to the assaults.
Reker later said the comments had been taken out of context.
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.
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.