In a statement, the Russiam Programme Director of Human Rights Watch Tanya Lokshina said: "It is hard to overstate just how vulnerable LGBT people are in Chechnya, where homophobia is intense and rampant".
The Chechen government has denied the reports.
The detention order allegedly came from the Republic's government, and Metro reports that Chechen leader Ramzan Kadyrov is "personally involved" in the process.
Reports of widespread persecution of homosexual citizens, including beatings, torture, and jailing them in concentration camps have emerged.
"We confirm what was said in Novaya Gazeta", Ms Poplevskaya said, while declining to name her sources in Chechnya.
The LGBT Network filed complaints with Russia's prosecutor-general, commissioner for human rights, and the Federal Investigative Committee, according to the BBC.
Svetlana Zakharova, a spokeswoman for the Russian LGBT network, told the Thomson Reuters Foundation by phone that "such campaigning against homosexual men is unprecedented in Russia".
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But Eristavi took issue with some media reports that referred to the Argun detention center as a "gay concentration camp", saying the center has been in use for some time to hold and torture various detainees - not just LGBTQ ones.
Despite an encouraging response from the worldwide community, no investigations into the detention of (perceived) gay men in Chechnya have yet been started, either at a local or federal level. He was detained by some security officials on suspicion of homosexuality.
Some men have reportedly been released severely injured, while others remain detained but exact details and numbers remain unclear.
"You can't detain and harass someone who doesn't exist in the republic", they said.
"I do really want the LGBTQ community in Russian Federation, including in Chechnya, to know that it has Canada's strong support", she said. "In our Chechen society, any person who respects our traditions and culture will hunt down this kind of person without any help from authorities", Saratova said, "and do everything to make sure that this kind of person does not exist in our society".
Ramzan Kadyrov says that, if gay men did indeed exist in Chechnya, authorities would not have to worry about them because their families would already be so ashamed of their sexual orientation that these individuals would thus be banished from the area by their relatives, and told never to return again.
Chechyna has opened the first concentration camp for homosexuals since Hitler, where campaigners say gay men are being tortured with electric shocks and beaten to death. Kadyrov is a thug who publicly supports honor killings.