Speaking to reporters aboard the plane taking him back to Rome from Armenia, he also said the Church should ask forgiveness for the way it has treated women, for turning a blind eye to child labour and for “blessing so many weapons” in the past.
In the hour-long freewheeling conversation that has become a trademark of his international travels, Francis was asked if he agreed with recent comments by a German Catholic cardinal that the Church should apologise to gays.
Francis looked sad when the reporter asked if an apology was made more urgent by the killing of 49 people at a gay club in Orlando, Florida this month.
He recalled Church teachings that homosexuals “should not be discriminated against. They should be respected, accompanied pastorally.”
He added: “I think that the Church not only should apologise... to a gay person whom it offended but it must also apologise to the poor as well, to the women who have been exploited, to children who have been exploited by (being forced to) work. It must apologise for having blessed so many weapons.”
The Church teaches that homosexual tendencies are not sinful but homosexual acts are, and that homosexuals should try to be chaste.
Francis repeated a slightly modified version of the now-famous “Who am I to judge?” comment he made about gays on the first foreign trip after his election in 2013.
“The questions is: if a person who has that condition, who has good will, and who looks for God, who are we to judge?”
Vatican spokesman Father Federico Lombardi said that the pope, by saying “has that condition”, did not imply a medical condition but “a person in that situation”.
In Italian, the word “condition” can also mean “situation”.
“We Christians have to apologise for so many things, not just for this (treatment of gays), but we must ask for forgiveness, not just apologise! Forgiveness! Lord, it is a word we forget so often!” he said.
Francis has been hailed by many in the gay community, but many conservatives have criticised him for making comments they say are ambiguous about sexual morality.
He told reporters on the plane “there are traditions in some countries, some cultures, that have a different mentality about this question (homosexuals)” and there are “some (gay) demonstrations that are too offensive for some”.
But he suggested that those were not grounds for discrimination or marginalisation of gays.
The pope did not elaborate on what he meant by seeking forgiveness for the Church “having blessed so many weapons”, but it appeared to be a reference to some Churchmen who actively backed wars in the past.