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.
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.
Waving German flags and signs meaning "Rapefugees not welcome", "Germany survived war, plague and cholera, but Merkel?", hundreds of PEGIDA supporters shouted "Merkel raus" (Merkel out).
In response, counter-protesters, separated by police, chanted "Nazis raus" at the site, where earlier, some 500 protesters, mostly women, had held a noisy rally against sexist violence.
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."
Ahead of the afternoon rally, Lutz Bachmann, co-founder of PEGIDA ("Patriotic Europeans Against the Islamisation of the Occident") posted a photo of himself online wearing a t-shirt saying "Rapefugees not Welcome".
In a similar vein, the populist right-wing Alternative for Germany party, which polls show as having 10 percent support ahead of state elections this year, claimed the violence gave a "taste of the looming collapse of culture and civilisation".
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.
Germany's conservative Die Welt newspaper said January 6, the day the scope of the violence became clear, "marks the beginning of a change in immigration policy" in an article outlining both "the benefits and the dangers of mass immigration from Muslim countries.
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