Archbishop Viganò has aligned himself with a conservative group of powerful prelates, in both the Vatican and the United States, who have seized on the clerical sex abuse scandal to try to damage Francis and his agenda. They believe the pope is abandoning the church’s rules and traditions through his shift away from culture-war issues like abortion in favor of an emphasis on inclusion, including toward gays, whom Archbishop Viganò and his allies blame for pedophilia in the church.

The archbishop writes that he was spurred to weigh in again by a New York Times article this past week quoting a Chilean abuse survivor, Juan Carlos Cruz. Mr. Cruz said Francis had told him that Archbishop Viganò sneaked Ms. Davis into the Vatican Embassy in Washington for a private meeting in 2015 and that the pope did not know who she was or why she was controversial.

Mr. Cruz recalled the pope saying to him, “I was horrified and I fired that nuncio,” or papal ambassador — a reference to Archbishop Viganò, who was the Vatican’s ambassador to the United States.

Archbishop Viganò writes in the new letter: “One of them is lying: either Cruz or the pope? What is certain is that the pope knew very well who Davis was, and he and his close collaborators had approved the private audience.”