ROME — For years, perhaps even centuries, it has been an open secret in Rome: That some prelates in the Vatican hierarchy are gay. But the whispers were amplified this week when Pope Francis himself, in a private audience, appears to have acknowledged what he called a “gay lobby” operating inside the Vatican, vying for power and influence.

The remarks — which the Vatican spokesman did not deny and the participants at the private audience confirmed — appeared to be part of an effort by the pope to take on the entrenched interests in the Vatican that many believe were a factor in why the previous pope, Benedict XVI, resigned unexpectedly. They appear to underscore numerous reports in the prelude to the election of the pope, that corruption, blackmail and violation of one of the highest codes of Catholic conduct were part of the intrigue that scandalized the Vatican in recent years.

Francis, who portrays himself as a simple pope of the people, has made it clear that one of his highest priorities is to put the Vatican’s house in order. He has appointed a group of eight cardinals to advise him on how to overhaul the Vatican, and the head of the Vatican Bank has recently given a series of interviews to journalists — an openness unheard of under his predecessors.

“It’s pretty incredible that the pope said these things,” said Sandro Magister, a Vatican expert at the Italian weekly L’Espresso. “I don’t think there’s any doubt on the foundation of the phrases attributed to him. Otherwise they would have denied it.”