German Chancellor Angela Merkel yesterday backed a toughening of expulsion rules for convicted refugees, as protesters took to the streets against a shocking rash of sexual assaults blamed on migrants during New Year's festivities.

Both women's groups and supporters of the xenophobic PEGIDA movement mobilised in separate rallies in Cologne, as 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.

"If the law does not suffice, then the law must be changed" she said, vowing action to protect not just German citizens, but innocent refugees too.

Outrage is growing in Germany over the revelations that hundreds of women ran a gauntlet of groping hands, lewd insults and robberies in mob violence last week in the western city on the New Year eve.

Most of the assailants were of Arabic or North African background, according to eye-witnesses, police and media reports.

The majority of suspects identified by federal police are also migrants, adding fuel to criticism of Merkel's liberal migrant policy -- which brought 1.1 million new asylum seekers to Germany last year.

Banging pots and blowing whistles, demonstrators waved signs in German meaning "No violence against women" and "No means no! It's the law!" while others read: "Protect our women and children."

The mob violence has played into popular fears, and threatened to cloud what had been a broadly welcoming mood in Germany where crowds cheered as Syrian refugees arrived by train in September.