Local newspaper Express reported that the attackers were members of rocker and hooligan gangs who via Facebook arranged to meet in downtown Cologne to start a "manhunt" of foreigners.
The assaults on women in Cologne and other German cities have prompted more than 600 criminal complaints, with the police investigation focusing on asylum seekers and migrants.
The assaults, ranging from theft to sexual molestation, have prompted a highly charged debate in Germany about Chancellor Angela Merkel's open-door policy on refugees and migrants, more than one million of whom entered the country last year.
Cologne police said a group of about 20 people attacked six Pakistanis on Sunday evening, injuring two of them. In another incident a few minutes later, a group of five people attacked and injured a Syrian man, police said.
On Monday, a regional parliamentary commission in the state of North-Rhine Westphalia, whose largest city is Cologne, will question police and others about the events on New Year's Eve.
The anti-Islam political movement, PEGIDA, whose supporters threw bottles and fire crackers at a march in Cologne on Saturday before being dispersed by riot police, will hold a rally in the eastern German city of Leipzig on Monday evening.
The attacks on women in Cologne have also sparked a debate about tougher rules for migrants who break the law, faster deportation procedures and increased security measures such as more video surveillance in public areas and more police.