German police has described a series of sexual assaults against women in Cologne on New Year's Eve as "a completely new dimension of crime."

Officers received numerous complaints from women who said they had been assaulted around Cologne's main train station next to the western German city's famous cathedral on the night from Thursday to Friday.

Cologne police chief Wolfgang Albers says witnesses described the assaults as coming from a group of up to 1,000 men whose appearance indicated they were of "Arab or North African origin."

Some 60 criminal complaints have so far been filed, including one allegation of rape.

German news agency dpa quoted Albers telling reporters on Monday that it was "an intolerable situation that such crimes are committed in the middle of the city."