Taking advantage of the New Year's Eve street party, hundreds of young men broke into groups and formed rings around young women, refusing to let them escape, the authorities said. Some groped victims while others stole wallets or cellphones.
Witnesses described the atmosphere around the city's central train station as aggressive and threatening, with firecrackers being thrown into the crowd in celebration. The women who were attacked screamed and tried to fight their way free, a man who had struggled to protect his girlfriend told German public television.
The Cologne police added that they had received 90 complaints from victims, including one who said she had been raped. No arrests have been made.
In Hamburg, the police said 10 women had reported that they were sexually assaulted and robbed in a similar fashion on the same night.
It was not clear that any of the men involved were among those who arrived in Germany over the past year from conflicts in Syria, Iraq, Afghanistan and elsewhere.
Chancellor Angela Merkel, in a statement, called the assaults disgusting. "Everything must be done to investigate as completely and quickly as possible those who are guilty and to punish them regardless of how they look, where they come from or what their background is," she said.
The assaults initially were not highlighted by the police and largely ignored by the German news media in the days afterward.
The attacks and the livid reaction to them presented a new political challenge for the chancellor, whose decision to take in refugees from conflict-ridden nations opened the doors to waves of migrants last summer and fall. As the number of asylum-seekers has grown and the challenge of assimilating them has become clearer, Merkel has come under intensifying criticism for failing to anticipate the social and economic costs of her policy.
The descriptions of the assailants - by the police and victims quoted in the news media - as being young foreign men who spoke neither German nor English immediately stoked the debate over how to integrate such large numbers of migrants and focused new attention on how to deal with the influx of young, mostly Muslim men from more socially conservative cultures where women do not share the same freedoms and protections as men.
The assaults set off accusations on the right and among some political commentators that the authorities and the news media had tried to ignore or cover up the attacks to avoid fueling a backlash against the refugees.
Far-right and anti-immigrant groups and other Germans who oppose the influx seized on the attacks, saying they demonstrated the dangers associated with accepting huge numbers of migrants.
"It is time to send a signal," said Christopher Freiherr von Mengersen, head of the nationalist Pro-NRW movement, based in the state of North Rhine-Westphalia. "We locals can no longer put up with everything that is being routinely swept under the rug based on a false sense of tolerance."
Even beyond the usual circle of anti-immigration activists, similar concern could be heard over whether the government's policy had come at too high a price to social stability.
"The government's loss of control is not only taking place on the borders," Alexander Marguier, deputy editor in chief of the monthly political magazine Cicero, wrote online. "For whoever gives up control of who enters the country no longer has control over the consequences of this action."
Henriette Reker, Cologne's mayor, who was stabbed during a campaign event in October by a German man who opposed her welcoming attitude toward migrants, sought Tuesday to play down the links to refugees, after meeting with police, state and city officials.
"There are no indications that this involved people who have sought shelter in Cologne as refugees," Reker said.
The assaults reported in Cologne were said to have taken place late Thursday in the city's main train station and the public square in front of it. The station was a central transit point for anyone coming or going from a fireworks display over the Rhine and the bars and nightclubs in the heart of the city, in the shadow of its landmark cathedral.
The police in Cologne say they believe several hundred men, ages 15 to 35 and visibly drunk, were involved in the violence that began when they tossed firecrackers into the crowd that thronged the square.
The police cleared the area shortly before midnight, blocking the main entrance to the station, in an attempt to control the situation, said Wolfgang Albers, Cologne's chief of police.
In the chaos that ensued after the square was cleared, the men appeared to have moved into the crowds, and that was when the assaults began. "Nobody knew where to go," Sascha Frohn, who said he was in the station on Thursday, told the public broadcaster WDR. "We stood with our backs to the wall and could see how people were robbed and German girls were groped. I was surrounded by a group of 50 to 60 people from Arabic countries. They would come up to us, shake hands and then try to reach into our bags."
Only after the square was reopened, after midnight, did the police begin receiving reports that women had been attacked.
With roughly 1 million people, Cologne is among Germany's most ethnically diverse cities, and it took in more than 10,000 refugees last year.
The city authorities said they would increase security after the assaults, including installing closed-circuit surveillance cameras, even as they urged anyone who videotaped the events on Thursday night to come forward.
But the situation quickly became as much about the politics of the situation as about the law enforcement response. Since the start of the year, Merkel has come under renewed pressure from within her own conservative bloc, with Horst Seehofer, head of the Bavarian sister party to the chancellor's Christian Democratic Union, calling for a cap of 200,000 refugees to be allowed into the country per year.
Calls came from the Bavarian Christian Social Union on Tuesday to deport any asylum-seekers found to be among the perpetrators in Cologne, a sentiment echoed by the left-leaning Suddeutsche-Zeitung, in a commentary that noted that German law provides for such a measure.
Yet the commentary, by Heribert Prantl, also warned against the risks of the debate taking on a poisonous tone that would only make integration of the many young refugees and immigrants legitimately in the country that much more difficult.
"The young men who come to Germany must begin working as quickly as possible," he wrote. "Work socializes. It is about our national peace, which is threatened by the excesses in Cologne and the excesses in the Internet."
Several hundred people gathered in front of Cologne's cathedral late Tuesday to protest violence against women. Several groups promoting women's rights have complained that the authorities have not taken complaints about sexual abuse of women in refugee shelters seriously enough.
To prevent further violence in Cologne during the coming Carnival celebrations, when thousands of costumed revelers throng the streets for the beginning of Lent, Reker said that city officials would work to help women protect themselves and to explain the city's attitudes and norms to newcomers.
"We will explain our Carnival much better to people who come from other cultures," she said, "so there won't be any confusion about what constitutes celebratory behavior in Cologne, which has nothing to do with a sexual frankness."