BERLIN — The mayor of Cologne has inflamed a debate in Germany about migrants and sexual harassment by suggesting that women can protect themselves from men on the streets by keeping them more than an arm’s length away.

The remarks by the mayor, Henriette Reker, were made Tuesday (Jan 5) to reporters after the Cologne police said they had received more than 90 complaints of robbery and sexual assault, including two accounts of rape, by groups of men who targeted young women in and around the city’s main train station in the crush of revelers on New Year’s Eve.

By yesterday, Ms Reker was being widely ridiculed by commentators and across social media for putting the onus on the victims of the attacks.

“It is always possible to keep a certain distance that is longer than an arm’s length,” Ms Reker told reporters Tuesday, suggesting that city authorities would provide guidelines for young women who find themselves surrounded by aggressive men attempting to grope them.

The police, who have yet to make any arrests, said the assaults had been carried out by several hundred young men, whom they described as having a “North African or Arabic” appearance.

The nature and scale of the assaults have shocked Germany and brought to the surface social tensions over the willingness of Chancellor Angela Merkel’s government to throw open the doors to more than 1 million refugees last year.

Ms Reker, who was elected last year, had already become a symbol of that embrace after being stabbed at a campaign event by a man angered over her welcoming attitude toward refugees. Her remarks have now made her a target of derision on all sides of the political spectrum.

Hundreds of women and men took to social media, posting angry responses and memes — including dozens showing the outstretched right arm known as the “Hitler Greeting” — under the hashtag #einearmlaenge, German for “an arm’s length.”

Even the country’s justice minister pushed back against the statement. “I don’t think much of tips for behaviour for women, such as ‘an arm’s length,’” Mr Heiko Maas wrote on Twitter. “Not women are responsible, but the perpetrators.”

The police have so far been unable to apprehend anyone, a fact that Mr Wolfgang Albers, Cologne’s chief of police, attributed to the chaos in which the assaults took place, despite there being dozens of officers on duty in the area.

“The women were in a very difficult situation,” Mr Albers said in an interview yesterday with public radio WDR 5. “They were afraid, they wanted to get away, and of course they did not notice any specific faces.”

In Hamburg, police said yesterday that they had received 53 complaints, more than half of them alleging sexual harassment, from victims aged 18 to 25. They appear to have been targeted in a similar fashion in that city’s Reeperbahn red light and club district on New Year’s Eve. Victims and witnesses in Hamburg also described the attackers as being dark-skinned or “looking Arabic.”

Although authorities have offered no concrete evidence that the attackers were among the hundreds of thousands of people who have poured into the country since mid-August, the incidents have laid bare the challenges Germans face in integrating young men from more conservative societies into their liberal, Western democracy.

Ms Christine Kronenberg, Cologne’s commissioner for women’s affairs, who attended a meeting Tuesday called by Ms Reker, said the mayor’s comments were “unfortunate.” She said they did not reflect her attitude toward women, or the victims.

“Sexual assaults are aimed at humiliating women and an expression of a male desire for power,” Ms Kronenberg said in a telephone interview. “Until now, we have encouraged women to defend themselves through resistance tactics, but these are all aimed at individual attackers.”

The New Year’s Eve mass-scale assaults, police said, involved groups of several men taking advantage of the crowds to target young women by surrounding them. While several perpetrators groped the women, others picked their pockets, stealing wallets and cellphones.

“This is a new phenomenon of a dimension that we have never been able to imagine before,” Ms Kronenberg said. “We now have to consider, together with police, new suggestions for how women can defend themselves in such situations.”

Even if authorities are able to apprehend suspects, the biggest challenge will be for victims to identify their attackers, given that several men appeared to have been involved in the attacks on each woman.

“It will be very difficult because it took place in a very crowded situation where many people were pushing to get in,” Mr Albers, the police chief, said. “And this situation was used by the perpetrators to carry out this horrible crime.” THE NEW YORK TIMES