The mayor of Cologne has summoned police for crisis talks after about 80 women reported sexual assaults and muggings by men on New Year's Eve.
The scale of the attacks on women at the city's central railway station has shocked Germany. About 1,000 drunk and aggressive young men were involved.
City police chief Wolfgang Albers called it "a completely new dimension of crime". The men were of Arab or North African appearance, he said.
Women were also targeted in Hamburg.
But the Cologne assaults - near the city's iconic cathedral - were the most serious, German media report. At least one woman was raped, and many were groped.
Most of the crimes reported to police were robberies. A volunteer policewoman was among those sexually molested.
Germany's New Year shock - by Damien McGuinness, BBC News Berlin
The pretty Christmas market and medieval setting may look idyllic, but at Christmas and New Year the area around Cologne Cathedral is a notorious danger zone when it comes to pickpockets and theft.
Now the sexual harassment, and in one case rape, of dozens of women has shocked Germany.
What is particularly disturbing is that the attacks appear to have been organised. Around 1,000 young men arrived in large groups, seemingly with the specific intention of carrying out attacks on women.
Police in Hamburg are now reporting similar incidents on New Year's Eve in the party area of St Pauli. One politician says this is just the tip of the iceberg.
And there are real concerns about what will happen in February when the drunken street-parties of carnival season kick off.
Cologne will stage carnival events in February, with hundreds of thousands of revellers expected in the streets, as on New Year's Eve.
The police chief said "the assailants' behaviour is a real concern for me, also because of the carnival".
Police were deployed outside the central station because of the crowds on New Year's Eve, but failed to spot the many attacks, according to reports. There are also fears that a number of women did not report assaults.
Cologne Mayor Henriette Reker said the attacks were "monstrous". "We cannot allow this to become a lawless area," she said, insisting that visitors could not come to the city fearing attack.
German Justice Minister Heiko Maas tweeted that "we won't tolerate these abhorrent assaults on women - all those responsible must be brought to justice".
One man described how his partner and 15-year-old daughter were surrounded by an enormous crowd outside the station and he was unable to help. "The attackers grabbed her and my partner's breasts and groped them between their legs."
A British woman visiting Cologne said fireworks had been thrown at her group by men who spoke neither German nor English. "They were trying to hug us, kiss us. One man stole my friend's bag," she told the BBC. "Another tried to get us into his 'private taxi'. I've been in scary and even life-threatening situations and I've never experienced anything like that."
The justice minister warned against linking the crimes to the issue of migrants and refugees.
Germany saw a record influx of migrants in 2015, which provoked an intense debate on immigration and marches by the anti-Islam Pegida movement.
Mr Maas said "the law does not discriminate regarding a person's origin or passport. All are equal before the law".
Cologne news website Koelner Stadt-Anzeiger says the suspects were already known to police because of frequent pickpocketing in and around Cologne central station.
In Hamburg several women told police that gangs of men had molested and robbed them on New Year's Eve on the Reeperbahn - a street known for its boisterous night life.
Some similar attacks were reported in Stuttgart.
A policeman who was outside Cologne station during the New Year's Eve trouble told the city's Express news website that he had detained eight suspects. "They were all asylum seekers, carrying copies of their residence certificates," he said.
However, there was no official confirmation that asylum seekers had been involved in the violence. Commentators in Germany were quick to urge people not to jump to conclusions.
German n-tv news says Cologne police are considering calling in reinforcements from other parts of Germany and installing extra surveillance cameras, with telescopic lenses.