Speaking to reporters on a flight back from Brazil, he reaffirmed the Roman Catholic Church's position that homosexual acts were sinful, but homosexual orientation was not.
He was responding to questions about whether there was a "gay lobby" in the Vatican.
"If a person is gay and seeks God and has good will, who am I to judge?"
He also said he wanted a greater role for women in the Church, but insisted they could not be priests.
The Pope arrived back in Rome on Monday after a week-long tour of Brazil - his first trip abroad as pontiff - which climaxed with a huge gathering on Rio de Janeiro's Copacabana beach for a world Catholic youth festival.
Festival organisers estimated it attracted more than three million people.
His remarks on gay people are being seen as much less judgemental than his predecessor's position on the issue.
Pope Benedict XVI signed a document in 2005 that said men with deep-rooted homosexual tendencies should not be priests.
But Pope Francis said gay clergymen should be forgiven and their sins forgotten.
"The Catechism of the Catholic Church explains this very well," Pope Francis said in a wide-ranging 80-minute long interview with Vatican journalists.
"It says they should not be marginalised because of this but that they must be integrated into society."
But he condemned what he described as lobbying by gay people.
"The problem is not having this orientation," he said. "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."
On the role of women in the Church, he said: "We cannot limit the role of women in the Church to altar girls or the president of a charity, there must be more.
"But with regards to the ordination of women, the Church has spoken and says no... That door is closed."
Answering questions about the troubled Vatican bank, he said the institution must become "honest and transparent" and that he would listen to advice on whether it could be reformed or should be shut down altogether.
"I don't know what will become of the bank. Some say it is better that is a bank, others that it should be a charitable fund and others say close it," he said.
Before leaving Brazil, Pope Francis gave a highly unusual one-to-one interview to a Brazilian TV programme.
The interview was shown on TV Globo's high-profile Sunday night documentary programme Fantastico, broadcast not long after the Pope departed for Rome.
The Pope was asked about the moment on his visit when his driver took a wrong turn and his vehicle was surrounded by crowds.
"I don't feel afraid," he answered. "I know that no-one dies before their time.
"I don't want to see these people who have such a great heart from behind a glass box. The two security teams [from the Vatican and Brazil] worked very well. But I know that I am undisciplined in that respect."
Asked about the recent protests by young people on the streets of Brazil, the Pope said: "The young person is essentially a non-conformist, and this is very beautiful.
"It is necessary to listen to young people, give them places to express themselves and to be careful that they aren't manipulated."
Asked about his simple lifestyle and use of a small car, he said it wasn't a good example when a priest had the latest model of a car or a top brand.
"At this moment I believe God is asking us for more simplicity," he added.