Merkel, who has so far refused to abandon her welcoming stance towards refugees, on Saturday had tough words for law-breakers.

It comes as Chancellor Angela Merkel says stricter laws regulating asylum seekers may be necessary.

Around 500 women staged a noisy protest Saturday in the German city of Cologne against a shocking rash of sexual violence during New Year's festivities that was blamed on migrants.

"If a refugee flouts the rules, then there must be consequences, that means that they can lose their residence right here regardless of whether they have a suspended sentence or a prison sentence", she said after a meeting with the top ranks of her CDU party.

Witnesses have said the assaults were perpetrated by men of "North African or Arab" appearance, inflaming a debate over Germany's ability to integrate about 1.1 million asylum seekers who arrived in 2015.

"This is in the interests of the citizens of Germany, but also in the interests of the great majority of the refugees who are here", she told party members.

Angela Merkel declared that refugees found to have committed a crime - even those who have not been given jail terms - should be required to leave Germany.

Water cannons and pepper spray have been used to push back thousands of anti-immigration protesters in Cologne as anger mounted in a demonstration following attacks on New Year's Eve.

After bottles and firecrackers were hurled at officials, police cancelled the march by the far-right groups, a spokeswoman said.

The German government said 31 suspects were briefly detained for questioning after the New Year's Eve trouble, among them 18 asylum-seekers.

Twenty-one people are being investigated for sexual assault, including nine Algerians, eight Moroccans, four Syrians, five Iranians, two Germans and one each from Iraq, Serbia and the US.

They documented 76 criminal acts, most them involving some form of theft, and seven linked to sexual molestation. "This did not happen at New Year so we need to take a stand. We should contribute to peace and understanding with courage and clarity, that is why I am here" said Anja Stiel, also from Cologne. He said police are trying to identify other suspects.

Almost two dozen asylum seekers were among those suspected of carrying out the attacks, police said this week, heightening tensions over immigration and fuelling criticism of Merkel's refusal to place a limit on the numbers of migrants entering the country.