Boris Johnson has said addressing the issue of so-called conversion 'therapy' is "complex" - as his government said it would bring forward plans to ban it in the UK.
The PM described the practice of trying to change someone's sexuality as "repulsive" and "abhorrent" when asked about it on a trip to Belfast on Friday.
Three advisers have quit over claims the government is a "hostile environment" for LGBT people, increasing pressure to take action.
But Mr Johnson said that although it was a "technically complex" problem, he was committed to making it conversion 'therapy' illegal.
"I think this practice is repulsive and I think it's abhorrent and I'm sorry these advisers have gone but be in no doubt that we will deal with this issue," he told reporters.
"It is technically complex to deal with but we're determined to take further steps to stamp it out."
On a visit to Scotland today, Equalities secretary Liz Truss, who has come under fire from the former LGBT advisers, promised prompt action.
"We're very committed to LGBT equality... and will shortly be bringing forward plans to ban conversion therapy, which is an abhorrent practice," she told ITV.
Ms Truss and her fellow equalities minister, Kemi Badenoch, have been accused of "dragging their feet" over the issue and have come under intense criticism for a "lack of engagement" on LGBT issues.
LGBT charities have been calling on the government for years to make steps to end the practice, which they say is "dangerous" and "harmful".
It has been more than two years since then-PM Theresa May promised to outlaw it in the UK as part of the government's LGBT action plan.
Jayne Ozanne, who resigned this week, said Ms Truss and Ms Badenoch were known within the LGBT community as "ministers for inequality".
"I don't believe that they understand LGBT people, particularly trans people," she told Sky News previously.
"I've sat in meetings and I've been astonished about how ignorant they are on issues that affect the real lives, particularly of younger people."
"I do not believe this Tory government, sadly, have the best wishes of the LGBT community at heart."
James Morton was the second LGBT adviser to quit before Ellen Murray said she was leaving "due to the government's persistent and worsening hostility towards our community in myriad areas".