Women hold up placards that read "Mrs. Merkel: Where are you? What are you saying? This worries us!" during a protest in front of the Cologne Cathedral, Germany, January 5, 2016. [Photo/Agencies]

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.

Merkel told Reker in a phone call the attacks deserved a tough response.

"Everything must be done to investigate those responsible as quickly and completely as possible and punish them, regardless of where they are from," she said, according to her spokesman.

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, Cologne mayor Reker said new steps would be take 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.