Rowan County , Ky., Clerk Kim Davis and Pope Francis. (Timothy D. Easley/AP; Max Rossi/Reuters)

The revelation of a private meeting last week between Pope Francis and Kim Davis, the Kentucky county clerk who refused to issue marriage licenses to same-sex couples, set off a vigorous debate in the United States on Wednesday about what message the popular pontiff may have been trying to send.

Unlike some of the other private sit-downs during the pope’s trip to the United States and Cuba, the Vatican declined to discuss the session with Davis, whose stance in the wake of the Supreme Court’s ruling affirming the right to same-sex marriage has made her a hero to some religious conservatives and a villain to many liberal activists.

“I do not deny that the meeting took place,” the Rev. Federico Lombardi, a Vatican spokesman, said after Davis’s attorney announced it in a news release. “But I have no other comments to add.”

The mystery further energized the debate over what Francis stands for, barely more than 48 hours after the pope flew home to Rome hailed as a moral authority who refused to be pulled into American culture wars.

Davis and her husband spent less than 15 minutes with the pope at the Vatican embassy in Washington last Thursday, her attorney, Mat Staver, said in an interview. Staver declined to say who initiated the get-together. He said Davis was already headed to Washington for the Values Voter Summit and arrived a day early in order to accommodate the papal meeting.

“He held out his hand and she clasped his hands and held them,” said Staver, founder and chairman of the Liberty Counsel, which represents Davis in her legal fight to avoid issuing marriage licenses to same-sex couples, an act that she says would violate her religious beliefs.

Staver said the pope and Davis, who was raised Catholic but became an Apostolic Christian four years ago, talked about bravery, then hugged and exchanged promises of prayer.

“She asked the pope to pray for her, and he said he would pray,” said Staver, who did not attend the meeting but saw Davis shortly afterward. “He said to ‘stay strong.’ ”

Francis held many private meetings during his six days in the United States, including with victims of sexual abuse and with Little Sisters of the Poor, the order of nuns suing the federal government over the contraceptive mandate in the Affordable Care Act.

Austen Ivereigh, a prominent Francis biographer, said he found it telling that the meeting with Davis was not publicly revealed until after the pope returned to Rome — and even then, it was Staver who announced it, not the Vatican.

The rosaries that Pope Francis reportedly gave to Kim and Joe Davis during a private meeting at the Vatican embassy in Washington on Sept. 24. (Liberty Counsel)

In contrast, church officials gave details about Francis’s visits with the nuns and the sex-abuse victims shortly after they happened.

With Davis, “I think the pope didn’t want to get into the specifics of the case,” Ivereigh said. “He wanted only to show support for religious freedom and the right of conscientious objection.”

The pope was politically careful throughout his U.S. trip, delving into hot-button issues including immigration and climate change but speaking broadly, inclusively and — for the most part — without specifics.

When he talked about religious freedom, for example, he linked it to nondiscrimination. When he talked about challenges to marriage, he widened the lens to include such issues as unemployment and low wages.

“I was surprised about how much he knew about the American context, whether it was history or whatever,” said Kathleen Sprows Cummings, director of the Cushwa Center for the Study of American Catholicism at the University of Notre Dame. “This is a man who did his homework.”

Since becoming pope in 2013, Francis has endeared himself to the LGBT community by meeting with a transgender man in Italy and, when asked about gay priests two years ago, answering, “Who am I to judge?”

News of Francis’s meeting with Davis exploded on social media, triggering strong reactions from the left and the right.

“Nooooooo!!!!!! This makes me so angry! So everything he’s preaching is a lie!!!” Alyssa Milano, the former star of “Who’s the Boss?” and “Charmed,” tweeted to her 2.85 million followers.

Francis DeBernardo, executive director of New Ways Ministry, which aims to build bridges between the LGBT community and the Catholic Church, said the Davis meeting threw a wet blanket over the pope’s U.S. visit.

“He sometimes talks out of both sides of his mouth,” DeBernardo wrote on his blog. “His remarks on specific moral and political issues are often at odds with his welcoming stance.”

Robert George, president of the U.S. Commission on International Religious Freedom, said he was thrilled to see the pope embrace Davis.

“I think he would stand up for anybody’s conscience rights, but I think [the meeting] probably increased the pope’s sense of the importance of the issue,” said George, who is Catholic.

Other prominent players in the religious-freedom movement — the term usually given to people who believe the rights of religious conservatives are threatened by liberal norms — seemed less willing to embrace Davis as a ­standard-bearer for their cause.

The Becket Fund, which is providing legal representation to the Little Sisters of the Poor, declined to comment on the pope’s meeting with Davis.

And Robin Wilson, director of the Family Law and Policy Program at the University of Illinois, said that by refusing to allow her deputies to issue marriage licenses, Davis denied civil rights to others even as she tried to protect her own.

“The pope intimated that this is a matter of conscientious objection, but it’s more complicated than that,” said Wilson, who was in Kentucky on Wednesday talking with lawmakers about how to find a compromise between gay rights and religious liberties. “What the pope should have said was: Of course she can keep her job and should be allowed to step aside over issues where there is a deep religious conviction. But she can’t deny others their civil rights, too.”

A Vatican official who spoke on the condition of anonymity said it would be rare for the Vatican to have initiated such a meeting, and added that it was likely suggested by “someone familiar with the Davis case and who enjoys the trust of the Holy Father.”

“Let’s not read too much into this,” the official said. “The meeting should not be understood as a blanket endorsement of the pope for all the things that Kim Davis says or does. Instead, it should be read as the support of the Holy Father for the right to conscientious objection.”

The Rev. James Martin, editor at large of America magazine, made a similar point online Wednesday.

“Not to put too fine a point on it, but Pope Francis also met [actor] Mark Wahlberg, and that does not mean that he liked ‘Ted.’ ”