DÜSSELDORF, Germany—A report presented Monday provided the strongest admission of errors to date in the Cologne police’s response to mass assaults on New Year’s Eve while raising new questions about security and migrants at the city’s annual Carnival celebration in just a few weeks.

Prepared by police, the report described how officers, overwhelmed and unable to assist victims, failed to call for backup as hundreds of people, mainly women, were robbed or sexually assaulted that night. Authorities say crowds of mainly migrant...