Germany must look again at deporting foreigners convicted of crimes following the Cologne sex attacks, Chancellor Angela Merkel says.
She said “clear signals” had to be sent to those not prepared to abide by German law.
Gangs of men described as of North African and Arab appearance were reported to be behind the attacks.
Meanwhile, similar incidents from New Year’s Eve have been reported in Finland and Switzerland.
“What happened on New Year is not acceptable,” Mrs Merkel said in a statement.
“These are repugnant criminal acts that a state, that Germany will not accept. The feeling women had in this case of being at people’s mercy, without any protection, is intolerable for me personally as well.
“That’s why it is important that everything that happened there will be brought to the table. We must examine again and again whether we have already done what is necessary in terms of deportations from Germany, in order to send clear signals to those who are not prepared to abide by our legal order.”
The identification of the attackers as North African or Arab in appearance has caused alarm in Germany because of the influx of more than a million migrants and refugees in the past year.
German Justice Minister Heiko Maas also said deportations “would certainly be conceivable” for any foreigners involved in the attacks.
He told the Funke newspaper group that German law allowed people to be deported during asylum proceedings if they were sentenced to a year or more in prison.
An internal police report published in German media on Thursday said officers “could not cope” with the volume of attacks in Cologne.
Women were “forced to run the gauntlet” through gangs of drunken and aggressive men outside the main railway station, it said.
The report recounts how police were met by “anxious citizens with crying and shocked children” when they arrived at the station.
“On the square outside were several thousand men, most of a migrant background, who were firing all kinds of fireworks and throwing bottles into the crowd at random.”
The number of reported crimes from the incident has risen to 121, police say, about three-quarters of which involve sexual assault. There were two allegations of rape.
Cologne police chief Wolfgang Albers has rejected claims that his teams were understaffed and described what happened as “a completely new dimension of crime”.
So far 16 suspects have been identified but there have been no arrests.
Similar attacks were also reported in Hamburg and in Stuttgart.
In Finland, police said they had received reports of “widespread sexual harassment” in Helsinki on New Year’s Eve.
A police official said they were tipped off that groups of asylum seekers had planned to sexually harass women and that three asylum seekers had been arrested.
“There hasn’t been this kind of harassment on previous New Year’s Eves or other occasions for that matter,” Helsinki deputy police chief Ilkka Koskimaki told AFP news agency.
“This is a completely new phenomenon in Helsinki.”
“I feel so ashamed” – Anger on Arab-language social media
Facebook user Israa Ragab: “Every time I watch the TV and hear them saying the suspects could be from North Africa or Arabs I feel so ashamed and disgusted”
Deutsche Welle Arabic journalist Nahla Elhenawy: “The ugliness of our region is reaching Germany”
@Farcry99 on Twitter: “Will Europe regret receiving people who suffer from religious and political repression?”
Arab social media fury at Cologne attacks
Police in the Swiss city of Zurich said about six women had reported being robbed and sexually assaulted on New Year’s Eve in attacks “a little bit similar” to those in Germany.
On Wednesday, Ralf Jaeger, interior minister for North Rhine-Westphalia, where Cologne is situated, said police had to “adjust” to the fact that groups of men had attacked women en masse.
He also warned that anti-immigrant groups were trying to use the attacks to stir up hatred against refugees.
Germany’s “anti-Islamisation” Pegida movement and the right-wing AfD party have said the attacks were a consequence of large-scale migration.
But Cologne’s mayor said there was no reason to believe those behind the attacks were refugees.