Kentucky Governor Steve Beshear on Tuesday called on county clerks who refuse to issue marriage licenses to gay and lesbian couples to resign.

The American Civil Liberties Union (ACLU) of Kentucky filed a class action lawsuit against Rowan County Clerk Kim Davis after she decided to stop issuing marriage licenses to all couples rather than serve gay couples.

Appearing in court Monday, Davis testified that she prayed and fasted for months over what would be her response to the Supreme Court's ruling striking down gay marriage bans in all 50 states.

She said that the First Amendment of the U.S. Constitution gives her the right to refuse to serve gay couples because it violates her religious faith.

“When you voluntarily decide to run for office, and you win, and you raise your hand and you take the oath to uphold the Constitutions of the United States … that oath doesn’t say, 'I will uphold the parts of the Constitution that I agree with and won't with the parts I don't agree with,'” Beshear said at a press conference.

“You can continue to have your own personal beliefs but you're also taking an oath to fulfill the duties prescribed by law. And if you are at that point to where your personal convictions tell you that you simply cannot fulfill your duties that you were elected to do, then obviously an honorable course to take is to resign and let someone else step-in who feels that they can fulfill those duties.”

A second clerk who is resisting the Supreme Court's authority, Casey Davis of Casey County, has said he will not resign.

(Related: KY clerk who refuse to issue marriage licenses to gays claims his rights are being violated.)