49-year-old Kim Davis says she objects to gay marriage on religious grounds and she filed the motion with the Sixth Circuit US Court of Appeals.
She was jailed earlier in September for refusing to carry out her duties.
Davis now argues that all the same-sex couples who sued her for a license received one from her deputies while she was in jail, so she says her office should not be required to issue them to any more couples once she returns to work.
But US district court judge David Bunning wrote that his mandate to issue licenses applied to all couples, not only those who filed suit.
Ms Davis' lawyer however said the the order was issued improperly has asked for a delay.
The Supreme Court legalised gay marriage all across the United States in June 2015, meaning officials in each state would have to issue marriage licenses to same-sex couples.
Ms Davis refused to do so and was declared to be in contempt of court - she was jailed for five days.
The appeals court has already dismissed Ms Davis' primary argument that her religious faith should exempt her from licensing a gay marriage.
If the court does not respond before she returns to work on Monday, she will have to decide whether to allow her office to continue issuing same-sex marriage licenses or again go against the orders of Judge Bunning who has sent her to jail once already.