The Chechen and Russian governments must investigate claims of persecution of gay men and protect LGBT rights, the US Holocaust Memorial Museum has said, as it condemned an alleged campaign of repression reported in Chechnya in recent months.

The museum's director, Sara Bloomfield, said: "The Holocaust teaches us what can happen when state-sponsored, group-targeted violence is allowed to go unchecked. The reports about the targeting of LGBT persons in Chechnya combined with statements from Chechen officials seemingly endorsing violence are cause for great concern."

Reports suggest Chechen leader Ramzan Kadyrov wants to "eliminate" the republic's gay community by the start of Ramadan on 26 May, according to the UK Foreign Office minister Sir Alan Duncan.

"Human rights groups report that these anti-gay campaigns and killings are orchestrated by the head of the Chechen republic, Ramzan Kadyrov," Sir Alan told Parliament.

More than 100 men have been rounded up and detained in secret prisons by authorities on suspicion of being gay in recent weeks, with many beaten and tortured, the Russian investigative newspaper Novaya Gazeta claimed. At least four are alleged to have been killed.

The Holocaust Memorial Museum recalled the purges of gay people in Nazi Germany during the rule of Adolf Hitler.

It said: "Gay men were targeted for persecution because they were viewed to be carriers of a 'contagion' that weakened society and did not contribute to the growth of the 'Aryan' population."