But “this was not a generic meeting in which Kim Davis happened to appear,” Mr. Staver said. The Davises snapped selfies inside the Vatican Embassy. However, he said, “out of deference and respect they didn’t want to pull out a cellphone with the pope. The Vatican had their own photographers there and we’re told the pictures will be released later.”

No photographs had been released by Wednesday evening in Rome.

Throughout his six-day American tour, Francis carefully navigated the country’s political divisions and seemed to be deliberately trying to strike a balance, if also to reframe entrenched debates. He spoke to Congress about the importance of “life” but elaborated on the theme by decrying the death penalty, not abortion. He also offered broad strokes about the importance of religious freedom — a big issue for American conservatives — but often in the context of preventing extremism and promoting interfaith tolerance.

Yet his meeting with Ms. Davis raises the question of whether the pontiff was again shifting directions, seizing on an issue — conscientious objection — typically embraced by liberals but instead framing it around Ms. Davis.

Francis did make an unscheduled visit to the Little Sisters of the Poor, an order of nuns suing the federal government over the contraception mandate of the Affordable Care Act. Reporters were not present at the meeting, which was announced later the same day by the Vatican spokesman, the Rev. Federico Lombardi. Asked on Wednesday why the Vatican noted that visit, but not the meeting with Ms. Davis, Father Lombardi drew a distinction.

“That meeting with the pope and the Little Sisters was a specific event,” he said, noting that he had informed the news media because the pontiff had diverted from his public schedule.

For the most part, Francis has avoided any incendiary talk about same-sex marriage, and early in his papacy he even signaled a tolerant attitude about homosexuals with his now famous comment, “Who am I to judge?” Francis opposes same-sex marriage and has often defined marriage as between a man and a woman. In his final Mass, in Philadelphia hours before his departure, Francis said that God is revealed through the “covenant of man and woman.”