MOREHEAD, Ky. — A Kentucky clerk who defied a federal judge’s order to issue marriage licenses and turned away four gay couples has until Monday to convince the judge to delay his mandate.

U.S. District Judge David L. Bunning rejected Rowan County Clerk Kim Davis’ claim that her Christian faith should exempt her from issuing marriage licenses to same-sex couples and ordered her on Wednesday to hand out the licenses. But her office kept denying them.

As the attorneys for gay and straight couples seeking a license warned they could request that she be held in contempt, Bunning ordered Davis to submit a final plea to stay his decision by Monday.

The fight in this eastern Kentucky college town began soon after the Supreme Court legalized gay marriage in June. Davis was among a handful of clerks across the country to cite her Christian beliefs and declare she would no longer hand out licenses to any couples, gay or straight.

Legal experts have likened the case to the resistance some local officials in the South put up five decades ago after the Supreme Court legalized interracial marriage.

“We’re going to keep coming back,” said Karen Roberts, shaking after she was denied a license to marry April Miller, her partner of 11 years. “We’re going to fight this to the very end.”

Three other couples streamed into the clerk’s office throughout the morning, and all were denied.

Staff in Davis’ office said she was on vacation. Though she has six employees authorized to issue licenses, deputy clerk Nathan Davis said the office was advised by its attorneys with the Christian law firm Liberty Counsel to continue refusing same-sex couples as it appeals the judge’s decision. They handed one couple who demanded an explanation a Post-it note with Liberty Counsel’s toll-free phone number.