Mat Staver, a lawyer for Davis, said the session lasted 10 minutes and was just between the Pope, his client and her husband. He said pictures were taken and will be released at some point.
"I was humbled to meet Pope Francis
. Of all people, why me?" Davis said in the statement.
"Pope Francis was kind, genuinely caring, and very personable. He even asked me to pray for him. Pope Francis thanked me for my courage and told me to 'stay strong.' "
Staver, who didn't attend the meeting, said the Pope hugged Davis and gave her and her husband each a rosary, which she in turn gave to her parents. Rosaries are common gifts from popes to visitors.
Davis' father and mother are lifelong Catholics. She is an Apostolic Christian after a religious conversion four and a half years ago.
The Vatican had little to say about the meeting.
"I don't deny that the meeting took place," said the Rev. Federico Lombardi, "but I have no comment to add."
The meeting added a partisan wrinkle to Pope Francis' trip last week.
While he strongly defended religious freedom in speeches at the White House, Congress and Philadelphia's Independence Mall, Francis avoided taking public stances on particular political issues.
Davis, meanwhile, personifies religious conservatives' concerns about the enforcement of nondiscrimination laws.
GOP candidate Mike Huckabee
cheered news of the meeting, saying that it amounted to an implicit endorsement of Davis.
Gay and lesbian Catholics called the Pope's meeting with Davis "puzzling"
and said it "throws a wet blanket" on his trip to the United States last week.
Francis DeBernardo, head of New Ways Ministry, an LGBT Catholic group, said the Pope sometimes seems to "talk out of both sides of his mouth" when it comes to gay rights.
For instance, the Pope has famously said "Who am I to judge" gay priests and urged bishops not to engage in constant culture war fights over same-sex marriage
"The time for vagueness, ambiguity, and secret meetings is over," DeBernardo said. "Pope Francis needs to state clearly where he stands in regard to the inclusion of LGBT people in the church and society."
During an inflight news conference on his way back to Rome on Sunday, Francis was asked about public officials refusing to carry out their duties as a matter conscience.
"I can't have in mind all cases that can exist about conscientious objection," the Pope answered. "But, yes, I can say the 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."
Asked whether that right also applies to 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."
While in Washington last week, Pope Francis also met with the Little Sisters of the Poor, nuns who are suing the Obama administration over the Affordable Care Act's contraception mandate. That meeting, too, took place behind closed doors.
A federal judge ordered Davis to jail this month over her refusal to issue marriage licenses to same-sex couples in the Kentucky county where she's clerk. Before being ordered to jail, Davis also refused to allow clerks in her office to issue licenses. She cited her biblical opposition to same-sex marriage.
Since her release, she has allowed the licenses to be issued but only with her name and title removed. Each license includes a statement saying it is issued "pursuant to a court order."