COPENHAGEN — Denmark, a country that regularly tops international indexes of gender equality and access to justice, is failing victims of rape, a new study shows.

The country has a “pervasive ‘rape culture’ and endemic impunity for rapists,” according to an Amnesty International report to be released on Tuesday about the Nordic nation, which has long been held up as a bastion for equality.

“While there is a widespread perception in Denmark that gender equality has been achieved,” the study says, “this report shows that in the area of sexual violence, Danish authorities must do more to live up to this positive image.”

Reporting rape to the police can be a difficult and humiliating challenge in the country, where women say they are still met with gendered stereotypes that focus on their clothing or actions rather than their attackers. Most perpetrators are men and a majority go free.