Police say around some 60 women reported being robbed, threatened or sexually molested at New Year celebrations in the western city of Cologne.

A series of New Year's Eve sex attacks blamed on Arab and North African men is threatening to fan the flames of Germany's refugee debate.

The wave of violence overnight last Thursday resulted in dozens of reports of sexual assault and robberies around the city's main train station, where a crowd of roughly 1000 men had congregated, police said, according to Spiegel online.

"We will not tolerate such cowardly and abhorrent attacks," German Justice Minister Heiko Maas said. "This is apparently an entirely new dimension of organised crime.

WOLFGANG RATTAY/REUTERS Women shout slogans and hold up a placard that reads "Against Sexism - Against Racism" as they march through Cologne.

"If a thousand people gather and commit the same violation, then there is some level of organisation involved," he said.

More than 90 criminal complaints were filed, and about a quarter of them cited sexual harassment or groping, with most others citing theft, Cologne Police Chief Wolfgang Albers said at a news conference. Small groups of men would emerge from the larger crowd to surround, harass and sometimes steal from women, the police chief said.

The crimes were committed by a group of men "who from appearance were largely from the North African or Arab world," Albers said.

WOLFGANG RATTAY/REUTERS A police vehicle patrols at the main square and in front of the central railway station in Cologne after the attacks.

Police said that they were previously aware of many of the men in the crowd, which did not include any recently arrived refugees. Similar attacks were reported in Hamburg and Stuttgart, according to the BBC.

Cologne Mayor Henriette Reker described the attacks as "outrageous" and called an emergency meeting of city officials, according to the Telegraph.

"We cannot tolerate a legal vacuum here," said Reker, who was elected last October while hospitalised after an opponent of her pro-refugee policies stabbed her in the neck.

WOLFGANG RATTAY/REUTERS Cologne Mayor Henriette Reker has promised new measures to stop violence in Cologne.

Officials throughout Germany walked a fine line in comments about the incidents, in an apparent attempt to distance the acts of a few from any entire group.

"In criminal law what's important is proving a crime, and everyone is equal before the law," Maas said. "It doesn't matter where someone comes from, it matters what they did and that we can prove it."

But others were more direct.

FABRIZIO BENSCH/REUTERS "This is obviously a new dimension in organised crime" ... German Justice Minister Heiko Maas addresses the Cologne assaults.

"We will not tolerate organised groups of men from North Africa that debase defenseless women with brazen sexual attacks," said Ralf Jaeger, interior minister of the state of North Rhine-Westphalia, according to Spiegel. "We owe that to women as well as to those North African refugees who want to live peacefully among us."

'IT CAN'T GO ON'

Germany has been inundated in recent months by refugees of the Syrian conflict. It has strained to accommodate and integrate the record number of refugees, leading to calls to more tightly control its borders.

"It can't go on like this," Steffan Bilger, a politician who belongs to German Chancellor Angela Merkel's party, tweeted, according the Local's translation. "Urgently needed: reduction of influx, secure borders, intensifying of deportations and meaningful justice. #Cologne."

With Interior Minister Thomas de Maiziere saying the perpetrators were "people apparently with a migrant background," the incident at the city's main train station has stoked Germany's debate about how to deal with a record number of asylum seekers as news reports and video of the melee spread.

Residents shouldn't harbour "blanket suspicion" against refugees fleeing to Germany to escape persecution, de Maiziere said.

Stephan Mayer, a lawmaker in Merkel's Christian Democrat-led bloc, suggested a possible link to the Cologne events.

"It would be terrible if such crimes were committed by some of those to whom we've generously taken into our country," Mayer, a member of the Bavaria-based Christian Social Union, said in a statement. "If it turns out that the majority of assailants indeed came from Arab or North African regions, that shouldn't be hushed up."

Merkel, who is facing criticism from the CSU and her own Christian Democratic Union for declining to cap the number of arrivals, reaffirmed her principled stance in her first public appearance of 2016.

"In our constitution, it says that human dignity is inviolable," she told carol singers at the chancellery in Berlin on Tuesday. "That applies not only to Germans and people who live in Germany" but worldwide, she said.

'TOUGH RESPONSE'

The right-wing Alternative for Germany (AfD), which has gained in polls in part at Merkel's expense thanks to a campaign against refugees, said she should close the border.

"Mrs Merkel, is Germany 'colourful and cosmopolitan' enough for you after the wave of crimes and sexual attacks?" tweeted AfD chief Frauke Petry.

There are almost daily attacks on refugee shelters.

"Events like that in Cologne foster xenophobia," said Roland Schaefer, head of Germany's association of towns and localities.

After a crisis meeting, Reker said new steps would be taken to avoid a repeat, including increasing police numbers at big events and installing more security cameras.

She stressed that women must feel safe at traditional carnival celebrations next month when the city closes down for five days of drunken street parades and parties.

Reker was stabbed in the neck and seriously hurt in October, just a day before she was elected mayor. Police said that attack appeared to be motivated by her support for refugees.

Reker said it was "unbelievable and intolerable what happened on New Year's Eve", but there was no reason to believe those involved in the attacks were refugees.

Officials said it would take time to bring the perpetrators of the New Year's Eve attack to justice, given the sheer size of the crowd, the time at which it occurred, and the foggy memories of witnesses, Spiegel reported.

For now, investigators were focusing on a small group of men from North African who have committed small-time robberies in the past.