Hundreds of women have reported they were groped and robbed by mainly North African suspects outside Colognes main train station where crowds had gathered to ring in the New Year.
Similar assaults, however, also took place that night in 12 of Germany's 16 regional states, according to the daily Sueddeutsche Zeitung and the NDR and WDR television stations, citing a report by German judicial police (BKA).
Contacted by AFP the BKA had no immediate comment on the report.
"The phenomenon of sexual violence, in part linked with robberies, is much greater than we previously thought," the newspaper said on its website, adding that the regional states were affected to different degrees.
The most affected state was North Rhine-Westphalia, which includes the city of Cologne, where 1,000 complaints have been filed, followed by Hamburg with 200.
In other states the number of reported incidents was lower: Hesse (31 complaints); Bavaria (27), Baden-Wurtlemberg (25), Bremen (11 and Berlin (6).
One case was reported in Lower-Saxony, Brandeburg, Saxony, Rhineland-Palatinate and Saarland.
Like Cologne the target of the assaults were women in almost all cases.
According to witnesses, the aggressors were often young men of foreign origin, between 17 and 30 years old.
The assaults in Cologne, which police have blamed on young men from North Africa and other Arab countries, have ignited a fierce debate over Chancellor Angela Merkel's policy of welcoming refugees to Germany which received one million asylum seekers in 2015.
On Saturday, Aydan Ozoguz, who handles integration issues for the government, told the Frankfurter Allgemeine Zeitung that the New Year's assaults had "poisoned" the atmosphere in Germany. "Several hundred criminals do not represent a million refugees," she said.