The Davis couple traveled to Washington and met the pope at the Vatican embassy last Thursday, ABC News and CBS News reported.
"It was really very humbling to even think that he would want to, you know, meet me or know me," Davis told ABC. "I put my hand out, and he grabbed it, and I hugged him, and he hugged me and he said, 'Thank you for your courage'."
"He told me before he left, he said, 'Stay strong.' That was a great encouragement," Davis said.
Davis said knowing that the pope agreed with what she was doing "kind of validates everything."
ABC said the pope gave Davis a rosary, which she plans to give to her Catholic parents.
The pope, speaking to reporters as he returned home from his 10-day trip to the United States and Cuba on Monday, said government officials had a "human right" to refuse to discharge a duty if they felt it violated their conscience.
Davis was jailed for five days in September for refusing to comply with a judge's order to issue the licenses in line with a U.S. Supreme Court ruling.