During an in-flight conference on his flight to Rome from the United States (U.S) the pontiff when asked about three-time divorcee Davis said: "Conscientious objection must enter into every juridical structure because it is a right."
Davis was imprisoned after refusing to issue the licenses to LGBT couples, despite same-sex marriage being legalised in the U.S in June, because it went against her Christian beliefs.
Francis made headlines last year for saying "who am I to judge" when it came to relationships.
According to The Independent New Ways Ministry, a U.S Catholic group campaigning for the Church to accept LGBT Christians, said: "Most remarkable about this comment is the absence of a condemnation of the marriage equality movement."
His words come before next month's Synod on the family in Rome.
Issues to be discussed include sexuality, civil marriages and the treatment of divorced Catholics within the Church.
Ahead of the October Synod, 11 conservative cardinals, led by Bishop Emeritus of Rome, Camillio Ruini, have released a new book that says the pillars of marriage and the family are under attack.
