Rowan County Clerk Kim Davis had stopped issuing all marriage certificates in mid-August following the high court's landmark June 26 ruling legalizing gay marriage in the United States.
Davis had filed suit in federal court, arguing that her Christian religious beliefs should exempt her from the ruling. A federal judge however disagreed.
Davis appealed the ruling to the Supreme Court and sought an emergency stay, but the court rejected her motion.
"We are not issuing marriage licences today," Davis said, according to footage recorded by a reporter for the local Courier-Journal newspaper.
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"Under whose authority?" demanded one of the men seeking to get married. He accused Davis of discrimination.
"Under God's authority," she replied.
"My beliefs cannot be separated from me," Davis added. "I'm willing to face my consequences, as you all will face your consequences when it comes time for judgment."
Kentucky Governor Steve Beshear in July ordered all county clerks to obey the Supreme Court's ruling and allow same-sex marriages to take place, or resign.
Today the American Civil Liberties Union filed a motion to find Davis in contempt of court for refusing to issue the licenses. ACLU said the court set a contempt hearing for Thursday.
"This is overwhelming. It feels ridiculous," said David Moore, who with his partner David Ermold was turned away by Davis, according to the daily.
Until the US Supreme Court's historic June ruling, the country's 50 states formed a legal patchwork: some states had already legalized gay marriage, while others were forced to do so by federal courts, and others had continued to ban it.