Ramesh Tawadkar, from Modi's Bharatiya Janata Party (BJP), announced plans to open up centres to treat gays and lesbians in the coastal resort state of Goa.
"We will make them normal. We will have centres for them, like Alcoholics Anonymous centres," Tawadkar told reporters Monday, adding that the Goa government would "train them and give them medicines too".
Tawadkar, Goa's sports and youth affairs minister, made the comments after releasing the state's policy on youth issues which listed lesbians, gays, bisexuals and transgenders (LGBT) as a stigmatised group that needed attention.
Tawadkar's comments drew widespread criticism and ridicule from gay rights groups who branded them offensive, while hostile remarks were posted on Twitter and other social media.
UN Secretary General Ban said laws against gay and lesbian relationships breed intolerance, although he did not refer specifically to India's colonial-era ban on gay sex.
Speaking on a visit to the capital New Delhi on Monday night, Ban said he "staunchly opposed the criminalisation of homosexuality".
"I am proud to stand for the equality of all people - including those who are lesbian, gay, bisexual and transgender," Ban said in an address to a gathering that included India's Nobel peace prize winner Kailash Satyarthi.
"I speak out because laws criminalising consensual, adult same-sex relationships violate basic rights to privacy and to freedom from discrimination. Even if they are not enforced, these laws breed intolerance."
India's Supreme Court reimposed a ban on gay sex in late 2013, ruling that responsibility for changing the 1861 law rested with lawmakers and not judges.
Gay sex had been effectively legalised in 2009 when the Delhi High Court ruled that banning "carnal intercourse against the order of nature" was a violation of fundamental rights.
Anjali Gopalan, founder of Naz Foundation, which first launched a case to decriminalise homosexual sex, called minister Tawadkar an "incompetent nincompoop".
"We should not respond to this kind of stupidity. If anyone needs treatment, it's people like him... he should realise he sounds like a complete fool," Gopalan told AFP.
Nitin Karani, trustee of the gay rights advocacy group Samapathik Trust, said the minister's comments reflected his ignorance, but at the same time he conceded that the LGBT community needed to "reach out more to the mainstream for awareness".
Members of the gay community have filed petitions to the top court since the 2013 ruling asking for a review on criminalising gay sex.
Campaigners say the law is rarely used to prosecute homosexual acts, but add that police do use it to harass and blackmail members of their already marginalised community.
Surveys show broad disapproval of homosexuality in India, forcing many gay men and women to live double lives.
Hindu hardliners have often called same-sex relationships a disease and a Western cultural import.
Popular Indian guru Baba Ramdev, who is close to the BJP, stirred controversy in 2011 when he said that homosexuality could be "cured" through yoga.
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