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!"
Education Secretary Michael Gove has condemned the use of the word 'gay' as an insult in schools.
Speaking at a education conference run by gay rights group Stonewall, Mr Gove said he thought that “language in playgrounds that wasn’t effectively policed.”
“It’s utterly outrageous and medieval to think that to use the word gay as an insult is somehow acceptable,” he said.
Michael Gove says he will look at how the law is policed #EdforAll
Conference attendees said the politician was challenged by singer Will Young over the handling of homophobic bullying in schools:
Brilliant to hear an exchange between Michael Gove and Will Young on tackling homophobic bullying. #edforall
Enjoyable face-off between Will Young and Michael Gove at Stonewall conference. I hearts you Will Young. In all the ways. ALL.
The Queen will sign the new Commonwealth Charter in an event on Monday after it received the support of every Commonwealth nation.
According to the Mail on Sunday, the charter which backs equal rights for women and gay people says:
We recognise that gender equality and women's empowerment are essential components of human development and basic human rights.
The advancement of women's rights and the education of girls are critical preconditions for effective and sustainable development.
The Government is introducing new legislation ending discrimination against women in the line of succession to the British throne.
The measure will mean that the Duke and Duchess of Cambridge's first baby can succeed to the throne, regardless of whether the child is a girl or a boy.
The Queen is set to sign a new charter backing equal rights for women and gay people in her capacity as head of the Commonwealth, a Buckingham Palace spokesman has confirmed.
– Buckingham Palace spokesman
At a Commonwealth event on Monday, the Queen will sign a charter agreed upon by the 54 members of the Commonwealth.
The Queen, as in all matters, is apolitical but is signing the document in her capacity as head of the Commonwealth.
The Mail on Sunday quoted one Royal Household source as saying: "The Queen takes her Commonwealth role very seriously. She has discussed the charter in detail with her advisers and understands it in full."
The Queen is set to sign a new charter backing equal rights for women and gay people after it received the support of every Commonwealth nation, it was reported tonight.
The monarch will sign the new Commonwealth Charter in an event on Monday which includes the core values - from human rights to the rule of law - that leaders have committed to upholding.
According to the Mail on Sunday, the document declares: "We are implacably opposed to all forms of discrimination, whether rooted in gender, race, colour, creed, political belief or other grounds.
Insiders said the decision to highlight the event is a "watershed" moment because it is the first time she has signalled her support for gay rights in her 61-year reign, the paper claimed.
The Queen is expected to sign the document at London's Marlborough House, the Pall Mall headquarters of the Commonwealth Secretariat on Monday, which is Commonwealth Day.
Gay rights groups have expressed their hopes that whoever is selected to replace Cardinal Keith O'Brien will do more to champion their cause.
The director of Stonewall Scotland, a charity that recently voted Cardinal O'Brien "bigot of the year", said he hoped a successor would "show a little more Christian charity towards openly gay people than the Cardinal did himself".
Tom French from the Equality Network said he hopes "that the Catholic Church in Scotland will use the opportunity new leadership brings to reassess its opposition to lesbian, gay, bisexual and transgender equality."