Hundreds of people gathered in Cologne Tuesday night to protest against the attacks.
"The perpetrators must be caught and brought to justice," said a woman, who gave her name as Manuela.
Police say more than a thousand men – many of them reportedly of northern African and Middle Eastern descent – had gathered in front of the cathedral on New Year’s Eve.
They threw firecrackers into the crowds - before splitting into groups and surrounding lone women, sexually assaulting and robbing them. Around 90 women have complained to police.
The attacks have poured fuel on the already-heated debate over immigration. Alexander Marguier – deputy editor of the political magazine Cicero – said via Skype from Berlin that many Germans are blaming the government's immigration policy.
“You have to see the fact also that this has not happened before. You know, such a big crowd in the main station of Cologne and also in other German cities, we haven’t seen this before. So there might be a link to this migration policy," said Marguier.
More than a million migrants arrived in Germany in 2015. Interior Minister Thomas de Maiziere said Wednesday it’s crucial to identify the attackers.
"General suspicions against refugees that are based on leads saying the perpetrators looked like people from North Africa are just out of place, but, we should not skip the debate about whether they are refugees or not," said de Maiziere.
In Hamburg, dozens of women were attacked in the city’s red light district, also on New Year’s Eve. Assaults were also reported in Stuttgart.
Police are trying to determine whether the attacks were coordinated. Lawmakers have called for any asylum seekers found among the attackers to be deported.