COPENHAGEN — Denmark’s ban on face veils in public took effect on Wednesday, setting off protests and reigniting a debate over a law that rights groups say discriminates against Muslim women.

The law, passed in May, does not specifically mention Muslim dress — it states that “anyone who wears a garment that hides the face in public will be punished with a fine” — but protesters say Muslim women are the intended target.

On Wednesday evening, women wearing the traditional Muslim face veil, known as a niqab, and full coverage burqas were joined by dozens of supporters wearing makeshift coverings and handkerchiefs tied across their faces at a protest in central Copenhagen. A simultaneous demonstration was held in the city of Aarhus.

And at the center of a protest for a woman’s right to cover up were women who didn’t. Bare legs, exposed shoulders and long blond hair mixed with head scarves and black veils.