In a show of defiance, a Kentucky clerk's office refused to issue marriage license to gay couples on Thursday despite a court ruling that ordered officials to follow the law and not their religious beliefs.

Rowan County Clerk Kim Davis has refused to issue any license to gay or even straight couples after the Supreme Court legalised same-sex marriage last June 26.

Five couples have filed a lawsuit in federal court as a result. Legal experts likened the situations to resistance by some officials in the South five decades ago when the Supreme Court legalised interracial marriage.

The Rowan County clerk's office refused to issue a marriage license to the couples hours after US District Judge David Bunning ruled against Davis and ordered her to discontinue her "no marriage licenses" policy.

Davis was not at her office last Thursday, but deputy clerk Nathan Davis said upon the advice of Liberty Counsel, the office's law firm in the case, the office will not be issuing marriage licenses.

"Kim Davis is just an example of what's going to be happening not only to other clerks but to other people who are going to be confronted with this issue, and we think that this is a serious matter that needs to be decided by a higher court, even the Supreme Court," said Liberty Counsel founder Mathew Staver.

The clerk's office also rejected the marriage license application of James Yates and William Smith Jr. Thursday for the second time.

They joined protesters after the clerk's office denied them a license.

Davis said issuing a same-sex marriage license with her signature violates her religious beliefs.

Judge Bunning said Davis violated the US Constitution's ban on the government establishing a religion by "openly adopting a policy that promotes her own religious convictions at the expenses of others."

"Davis remains free to practice her apostolic Christian beliefs. She may continue to attend church twice a week, participate in Bible study and minister to female inmates at the Rowan County Jail. She is even free to believe that marriage is a union between one man and one woman, as many Americans do," Bunning wrote. "However, her religious convictions cannot excuse her from performing the duties that she took an oath to perform as Rowan County Clerk."

Lawyers for the same-sex couples who failed to obtain marriage licenses are considering asking the judge to hold Davis in contempt that could land her in jail or subject her to a fine.