While admitting that the Pope's change in tone about gay priests is a "small step" that "does matter," Richard Lane from gay rights group Stonewall told ITV News there was much more to be done.
A next step would be a "strong statement against the harassment and persecution of gay people around the world [from the Pope]," Mr Lane said.
"He's got an unprecedented position at the Church with over a billion people so for him to make that statement would be incredibly significant."
Gay rights group Stonewall told ITV News it is baffled by the Pope's comments on gay priests.
– Richard Lane, Stonewall External Affairs Officer
While many lesbian, gay and bisexual Catholics will no doubt welcome this change in tone, the Pope’s criticism of those who lobby for gay equality sounds baffling when his Church still lobbies ferociously worldwide against gay people’s basic human rights.
Stonewall had objected to a section of the Pope's comments which had followed headline remarks about not wanting to judge priests who are gay:
"The problem is not having this [homosexual] orientation. We must be brothers. The problem is lobbying by this orientation, or lobbies of greedy people, political lobbies, Masonic lobbies, so many lobbies. This is the worse problem," he had said.
Pope Francis addressed journalists in a remarkably relaxed manner at a press conference aboard the Papal Aircraft.
He tackled the sensitive issues of gay priests, women priests and the problems of paedophilia within the Roman Catholic Church.
ITV News Correspondent Paul Davies reports:
Pope Francis reached out to gay people in his first news conference, which was held aboard the papal plane as he returned to Rome from his historic maiden trip overseas to Brazil.
Pope Francis told reporters he would not judge priests for their sexual orientation: "If someone is gay and he searches for the Lord and has good will, who am I to judge?"
The pontiff's words signal a move away from the views traditionally held by the Roman Catholic Church - his predecessor, Pope Benedict XVI, authored a document that said men with deep-rooted homosexual tendencies should not be priests.
During his 90-minute news conference the pope appeared relaxed and smiled frequently as he answered every question.
The pontiff even thanked the journalist who raised allegations reported by an Italian newsmagazine that one of his trusted monsignors was involved in a scandalous gay tryst.
Francis said he investigated and found nothing to back up the allegations.
Once he had returned to Rome, Francis tweeted to his 2.7 million followers: "I am back home, and I assure you that my joy is much greater than my exhaustion!"