Casey Davis, one of three clerks in the state who is not granting licenses, held a meeting with Gov. Steve Beshear after last month's ruling that upheld equal right to marriage across the country.
However, Beshear insisted clerks must carry out their duties and said the majority were "complying with the law" despite personal beliefs.
Image: Casey Davis and wife Christy
Casey County Clerk Casey Davis, center, speaks to the media with wife Christy at his side before meeting with Gov. Steve Beshear in Frankfort, Kentucky, on Thursday. Pablo Alcala / AP

"'Issue marriage licenses or resign' — those were the words," Davis told reporters after the meeting. "I can't quit … I have a mortgage to pay."
A YouTube video of two men being denied a marriage license in Rowan County by clerk Kim Davis has been viewed more than 1.5 million times.


Among Davis' supporters outside Thursday's meeting was a representative of the Family Foundation of Kentucky which has established a fund "for the legal defense of those who are targeted to have their religious liberty curtailed."
Gov. Beshear did not speak to reporters but issued a statement that said state officials "must recognize same-sex marriages as valid and allow them to take place."
The statement added: "One of Mr. Davis' duties as county court clerk is to issue marriage licenses, and the Supreme Court now says that the United States Constitution requires those marriage licenses to be issued regardless of gender."
"While there are two or three county court clerks still refusing to perform their duties, the rest of the county court clerks are complying with the law regardless of their personal beliefs," it said, warning: "The courts and the voters will deal appropriately with the rest."

 
Casey Davis told reporters that he would neither issue marriage licenses nor resign, according to NBC station WAVE. "Nature's law will supersede any law that man puts on a piece of paper," Davis said, according to the station. "My job cannot go beyond what my conscience allows."
Earlier this week, Davis proposed the automatic issue of marriage licenses online as a workaround so that clerks did not have to be involved.
"We bank online. We buy groceries online. ... We buy hunting and fishing licenses online. I think that we can buy marriage licenses online," he told The Associated Press. "And that relieves the 120 county clerks of this state."