Berlin (AFP) - German leaders expressed shock over dozens of apparently coordinated sexual assaults against women on New Year's Eve in the western city of Cologne blamed on "Arab-looking men," but warned against anti-migrant scapegoating.

Chancellor Angela Merkel called for a thorough investigation of the "repugnant" attacks, ranging from groping to at least one reported rape, allegedly committed in a large crowd of revellers during year-end festivities outside the city's main train station and its famed Gothic cathedral.

Merkel's spokesman Steffen Seibert said she had called Cologne's mayor, Henriette Reker, to express her "outrage" over the violence, which she said required "a tough response from the state".

"Everything must be done to find as many of the perpetrators as possible as quickly as possible and bring them to justice, regardless of their origin or background," Seibert quoted Merkel as saying.

Police in Cologne said they had received 90 criminal complaints by Tuesday and quoted witnesses as saying that groups of 20-30 young men "who appeared to be of Arab or North African origin" had surrounded victims, assaulted them and in several cases robbed them.

Germany took in around one million asylum seekers in 2015, many of them fleeing war-ravaged Syria.

A plain-clothes policewoman was reportedly among those attacked.

"We assume more people will come forward," police chief Wolfgang Albers told reporters.

The northern port city of Hamburg also reported around 10 similar attacks.

On Tuesday evening 200-300 people, according to police estimates, gathered in front of Cologne cathedral calling for more respect for women.

One female demonstrator held a sign reading: "Mrs. Merkel, what are you doing? This is scary".

Interior Minister Thomas de Maiziere lashed out at Cologne police for failing to stop the assaults.

"The police cannot work in this way," de Maiziere told public TV channel ARD.

Police said they evacuated the area because of fears people could be injured by fireworks -- and admitted the assaults then began without them realising what was happening.

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"It is not acceptable that the square could be evacuated and then (the attacks) take place" in the same location, with officers "waiting for complaints" from victims before taking action, de Maiziere said.

"I am urgently demanding clarification."

- 'Exploitation' of refugee issue -

Justice Minister Heiko Maas said the assaults represented "a new dimension of crime that we will have to get to grips with," adding that they had appeared to be "coordinated".

Asked by a journalist whether refugees were behind the rampage, Maas said police were still working to identify the attackers.

"This is not about where someone is from but what they did," he said.

"Making an issue out of it, lumping it together with the refugee issue, is nothing but exploitation. Now is the time to determine the facts and then decide on the necessary consequences."

Meanwhile the right-wing populist Alternative for Germany (AfD) party, which hopes to gain seats in three regional elections in March, seized on the attacks as "a result of unchecked immigration".

"Here we see the appalling consequences of catastrophic asylum and migration policies on Germany's everyday reality," party leader Frauke Petry said.

The Cologne daily Koelner Stadt-Anzeiger said many of the suspects were already known to police due to a rash of pickpocketing and muggings near the railway station.

- 'It was terrible' -

Victims described terrifying scenes in the marauding mob.

Katja L., 28, said she was with three friends outside the station when they encountered a group of "foreign-looking men".

"Suddenly I felt a hand on my bottom, then on my breasts, then I was groped everywhere," she told Cologne tabloid Express.

"It was horrible. Although we screamed and flailed about, the guys didn't stop. I was beside myself and think that I was touched about 100 times across around 200 metres (yards)."

A woman in her 30s interviewed on rolling news channel N24 said she was groped by a group of "Arab-looking men".

"They didn't look at me aggressively, they seemed more curious than anything, and a little drunk," she said.

"I was furious."

Cologne mayor Reker, who was stabbed in the neck in October in an attack apparently over her welcoming stance toward refugees, called a crisis meeting with political officials and police Tuesday after the case made national headlines.

She pledged to step up security and violence-prevention measures ahead of next month's raucous Carnival, which draws hundreds of thousands to party in the city's streets.

Albers said security cameras and better lighting would be installed for the February 4-10 event, including around the main rail station.

Merkel in her televised New Year's address called on Germans to continue to welcome refugees despite mounting criticism and to reject far-right ideologues whipping up anti-migrant sentiment.