At the start of the week, prosecutors had reported 516 police reports by alleged victims of groups of men of "Arab or North African appearance" who groped and robbed women in a large crowd of revellers in the city centre. Two rapes were also reported.
"That represents a slight rise in the total," a spokesman for the public prosecutor's office in the western city told AFP.
He said the 561 complaints covered 653 alleged criminal offences. In previous reports, authorities had said that about 45 percent of the crimes were of a sexual nature.
Authorities told DPA news agency that criminal probes had been opened against 12 North African suspects, of whom five were being held in custody.
The case has inflamed tensions in Germany, which took in nearly 1.1 million asylum seekers in 2015, mainly from Syria, Afghanistan and Iraq, and put pressure on Chancellor Angela Merkel for her welcoming stance toward refugees fleeing war.