About 521 complaints allege some kind of sexual assault, including three rapes. The overall number of complaints has grown from 766 on Monday to 809 on today.
The attacks have stoked a fierce debate in Germany about how to integrate the almost 1.1 million asylum-seekers who arrived last year.
German news agency dpa reported Tuesday that police are investigating 21 people from North African countries in connection with the Cologne attacks for robbery, theft and trafficking stolen goods. Eight suspects are currently in detention. One of them is accused of sexual assault for allegedly groping a woman.