Davis and her husband Joe met with the pope at the Vatican Embassy in Washington, D.C., on Sept. 24, according to a statement from the Liberty Counsel.
The Vatican Press office has not confirmed or denied that the meeting occurred, and the Apostolic Nunciature in Washington, D.C., has not commented on the matter.
ABC News' Terry Moran asked Francis Sunday night if he supports individuals, including government officials, who claim religious liberty as a reason to disobey the law.
Francis responded, "I can't have in mind all the cases that can exist about conscientious objection, but, yes, I can say that conscientious objection is a right that is a part of every human right. It is a right. And if a person does not allow others to be a conscientious objector, he denies a right."
When asked if that includes government officials, Francis said, "It is a human right and if a government official is a human person, he has that right. It is a human right."
Earlier this month Davis was jailed for nearly one week after she refused a judge's order to issue marriage licenses in Rowan County, Kentucky, to same-sex and heterosexual couples. When Davis returned to work, she said she wanted her name and title removed from the licenses being issued by her office.
Last week Davis told ABC News' Paula Faris that she feels her Christian beliefs trump her day-to-day responsibilities.
"My constituents elected me. But the main authority that rules my life is the Lord," she said.
Davis' stance has drawn intrigue, reverence, scrutiny and scorn. She has been called Hitler and a homophobe, she said.
"What people say about me does not define who I am. That's everybody's opinion and that's everybody's right," Davis said.
"I've been called things and names that I didn't even say when I was in the world. Those names don't hurt me," Davis added. "What probably hurt me the worst is when someone tells me that my God does not love me or that my God is not happy with me, that I am a hypocrite of a Christian."