Her advice, offered in response to a question about what women in Cologne can do to protect themselves, came during a news conference at which Reker issued her first public comments over reports from about 90 women alleging sexual harassment and thefts on New Year's Eve.
A crowd of about 1,000 men — described by the city's police chief as being "largely from the North African or Arab world" — had reportedly gathered outside the main train station that night. Small groups broke away from that crowd throughout the night to surround and harass women. At least 106 criminal complaints have been filed,up from 90 on Tuesday, the Associated Press reported.
"At least three quarters have a sexual component. In two cases we are investigating crimes that amount to rape," Cologne police spokesman Christoph Gilles said. Previous reports cited officials saying the majority of complaints cited thefts.
Authorities say the assaults may be linked to a crime ring in nearby Düsseldorf, the Associated Press reports. Over the past two years, criminals there have groped women to distract them while they are being robbed, officials said.
Authorities also said that they have identified at least 2,000 suspects of North African origin in connection with such organized attacks since 2014, according to the report. They have identified three suspects in the New Year's Eve incidents, though no arrests have been made, a state official told a Germany news agency.
Reker's "arm's length" comment was just one piece of a larger "code of conduct" proposed for young women and girls that the mayor said would soon be available online, according to the German broadcaster Deutsche Welle. Other suggestions included keeping away from large public events, sticking to groups and asking bystanders for help if needed.
Although she also suggested a similar code of conduct for those from other cultures who plan to participate in Carnival celebrations, Reker's comments on the code for women immediately elicited a backlash online.
One politician, Christopher Lauer, tweeted, “Man: “I had intended to mug this woman and molest her, but s***! She’s an arm’s length away from me!” according to the Guardian. The hashtag #einearmlänge — which translates as "an arm's length" — was one of Germany's top-trending hashtags late Tuesday, according to Deutsche Welle.
More broadly, German media and officials have weathered criticism for their slow and lackluster response to the incidents, with some alleging that the cause for the lag was hesitance to act for fear of inflaming the country's debate on refugees.
Reker, who was stabbed in the neck last fall by a man who reportedly disagreed with her liberal stance on refugees, has warned against linking the New Year's Eve attacks to migrants. Interior Minister Thomas de Maizière echoed that note of caution, though he added that political correctness should not obscure the debate, the BBC reported.
"If North Africans were the perpetrators, for which there is some indication, there should not be a taboo and people should not gloss over it," de Maizière said.
German public broadcaster ZDF apologized for not covering the story sooner while hundreds protested in Cologne on Wednesday. As many as 300 women held a demonstration near where the attacks occurred, some holding signs calling for Chancellor Angela Merkel to get involved.
Cologne police, who reportedly have few leads in the incidents, came under fire for their purported inadequate response, but Police Chief Wolfgang Albers said Wednesday that he would not step down.
This post was updated at 3:30 p.m.