UK minister tells LGBTQ fans to respect Qatari laws at World Cup
Homosexuality is illegal in the Gulf state, where the tournament begins on November 20.
"One of the things I would say for football fans is, you know, please do be respectful of the host nation," Cleverly told LBC radio on Wednesday.
"They are trying to ensure that people can be themselves and enjoy the football, and I think with a little bit of flex and compromise at both ends, it can be a safe, secure and exciting World Cup."
Three Lions Pride, a LGBT England fan group, described Cleverly's comments as "an extremely unhelpful intervention."
In a statement, Three Lions Pride added: "To insinuate that an acceptable and proportionate safety measure is to 'be less queer' forces us back into the closet and risks mental health crises."
Labour's shadow culture secretary Lucy Powell described the remarks as "shockingly tone deaf".
Qatar has also faced criticism for its human rights record on the treatment of foreign workers on major infrastructure projects for the World Cup.
Captains from a number of leading European countries, including England, France and Germany, will wear armbands in rainbow colours with the message "One Love" in an anti-discrimination campaign during the World Cup.