Three French gay rights groups have accused the Russian republic of Chechnya of a policy of genocide towards gay people in a complaint filed at the International Criminal Court.
They have blamed Chechen President Ramzan Kadyrov and state officials for a "wave of persecution".
They cited the case of a teenaged male thrown out of a ninth-storey window, allegedly because of his sexuality.
Chechen officials have denied that gay people even exist in the republic.
Russian President Vladimir Putin earlier this month backed an inquiry into the reported crackdown on gay people in Chechnya.
But the three French groups have rejected Russia's internal investigation, and want the International Criminal Court in The Hague to start work before Russia withdraws from its jurisdiction in November.
Reports of arbitrary arrests of gay men first surfaced last month in the Russian newspaper Novaya Gazeta.
The three groups highlighted the case of a 17-year-old gay youth allegedly thrown to his death from a ninth-floor window by an uncle supposedly anxious to salvage the family's honour.
They have accused President Kadyrov of setting up torture camps to exterminate homosexuals, Le Monde (in French) reported. It quoted the leader of Idaho France - one of the three groups instigating the ICC case - as saying the court was the only way they could pursue their grievances.
Last week five gay rights activists were detained in Moscow as they tried to deliver a petition to the office of Russia's prosecutor general.
Police said they were held because their action was unauthorised.
The activists said more than two million people had signed the petition to investigate alleged torture and detentions of gay people in Chechnya.
President Kadyrov has insisted that there are no "people of non-traditional orientation" (a term sometimes used to describe LGBT people in Russia) in the predominantly Muslim republic.
Chechen officials also say the local police have not received any official complaints from alleged victims.