The Charity Commission for Northern Ireland has been urged to review the charitable status of Core Issues Trust, a Christian organisation which campaigners claim promotes "conversion therapy" for gay people.
The National Secular Society (NSS) has written to chief charity commissioner Nicole Lappin, Communities Minister Deirdre Hargey and Health Minister Robin Swann over the issue.
In its letter, the NSS wrote: "Given that this practice can cause individuals significant mental health issues and harms society by reinforcing stigmas against LGBT+ people, we believe a clear tension exists between the public benefit requirement and the promotion of 'conversion therapy'.
"Organisations that serve no clear public benefit - or worse, cause harm by actively promoting 'conversion therapy' - risk fundamentally undermining public confidence in the charitable sector."
The society added that a provision which makes "the advancement of religion" a charitable purpose should be re-evaluated.
NSS chief executive Stephen Evans said: "Bogus therapies which encourage people to change or suppress their sexuality are harmful and widely discredited. Those promoting them shouldn't enjoy the tax breaks and public recognition that charitable status brings."
The Charity Commission said the letter will be considered in detail.
"The purpose of charity law is not to say if a certain belief is right or wrong. The definition of a charity in law says that you must be established for exclusively charitable purposes," a spokesperson said.
"A purpose must be beneficial, not harmful. If any organisation, including a religious one, requires improper pressure to be placed on people to remain within that organisation against their will, or completely withdraw from society, then there is likely to be more harm than benefit.
"A purpose must also not promote hatred towards others who do not share the same religion. The commission is considering in detail the issues raised."
A spokesman for Core Issues Trust said it would welcome active engagement with the Charity Commission.
"Core Issues Trust supports counselling choice for individuals whether they are from no-faith, other-faith or are Christian believers, who seek to live according to primary, personal values," the spokesman said.
"We look forward to engaging with the commission in respect to the matters raised by the NSS."