A group of around 40 Chechens are now in hiding in other parts of Russia, Russia LGBT Network spokesperson Svetlana Zakharova told BuzzFeed News, and are having difficulty securing visas that would allow them to flee the country.
"As visa records are confidential under USA law, we are unable to discuss individual cases", they said.
Lithuania's foreign minister says the Baltic nation has given refuge to two gay men from Chechnya following reports of a campaign of torture and abuse against homosexuals in the southern Russian region.More news: Hamish Bennett relishes solid comeback for Kiwis
On April 1, Russia's Novaya Gazeta daily raised the issue of gay people's civil rights being violated in Chechnya.
Kadyrov denies the allegations and has said that homosexuality does not exist in Chechen society.
On April 20, Russian Presidential Spokesman Dmitry Peskov told reporters that allegations about the persecution of LGBT people in Chechnya were groundless. Others were returned to their families barely alive from beatings.
Human Rights Watch later confirmed the horrific reports, adding that the information coming through was "consistent" with "numerous trusted sources" they had spoken to on the ground in Russian Federation.
On May 5, Moskalkova informed Russian President Vladimir Putin that she had been tackling violations of LGBT people's rights and asked him to issue instructions on setting up an inter-agency working group that would be active in Central Russia instead of Chechnya and receive people's requests if any were made. And in April, Nikki Haley, the USA ambassador to the United Nations said that if these claims are true, that "this violation of human rights can not be ignored".