A federal appeals court has denied a motion by a Christian county clerk in Kentucky for a stay of the preliminary injunction issued by a lower court that ordered her to resume issuing marriage licenses to all couples regardless of their sexual preferences.

Rowan County Clerk Kim Davis stopped issuing marriage licenses to all couple applicants after the US Supreme Court legalised same-sex marriage last June.

"In light of the binding holding of Obergefell, it cannot be defensibly argued that the holder of the Rowan County Clerk's office, apart from who personally occupies that office, may decline to act in conformity with the United States Constitution as interpreted by a dispositive holding of the United States Supreme Court. There is thus little or no likelihood that the Clerk in her official capacity will prevail on appeal," the US 6th Circuit Court of Appeals ruled on Wednesday.

Rowan was sued by the American Civil Liberties Union (ACLU) in Kentucky after she refused to issue marriage license to same-sex couples, on the ground that such an act would violate her religious beliefs.

Davis said the issuance of the license to same-sex couples would be an endorsement of gay marriage, which she strongly objects on religious grounds.

In a ruling last Aug. 12, US District Judge David Bunning ordered Davis to resume issuing marriage licenses.

He said the "State is not asking [Davis] to condone same-sex unions on moral or religious grounds, nor is it restricting her from engaging in a variety of religious activities."

"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. However, her religious convictions cannot excuse her from performing the duties that she took an oath to perform as Rowan County Clerk. The Court therefore concludes that Davis is unlikely to suffer a violation of her free exercise rights under Kentucky Constitution," Bunning said.

Davis sued Kentucky Gov. Steve Beshear after he issued a letter that all county clerks must issue marriage licenses to gays based on the US Supreme Court ruling.

"Neither your oath nor the Supreme Court dictates what you must believe. But as elected officials, they do prescribe how we must act," he said.

Reacting to the appeals court ruling, ACLU Kentucky Legal Director William Sharp said, "While government employees do not give up their religious liberty upon accepting public employment, they cannot withhold government services because they have personal religious objections to individuals receiving those services," adding that "properly understood, religious liberty is a shield that protect individuals from the government, not a sword with which the government, through its employees, may impose particular religious views on others."

Following the court of appeals ruling, Davis through Liberty Counsel on Friday filed an emergency application to stay preliminary injunction pending appeal before the US Supreme Court.

"Religious liberty is neither absolutely surrendered at the entry door of public service nor waived upon taking an oath of office. To suggest otherwise creates a religious (or anti-religious) test for holding office – which the United States and Kentucky Constitutions expressly forbid," Liberty Counsel stated.