Attorneys for the Kentucky clerk who was jailed last week because of her refusal to issue marriage licences to gay couples said Monday they have filed an emergency motion with a federal court that they hope will result in Kim Davis' freedom.

The filing seeks to have Kentucky Gov. Steve Beshear accommodate Davis' "religious conviction," and not compel her to grant licences to gay couples, Liberty Counsel said in a statement.

"The motion requests an injunction pending appeal for an exemption from the Governor's mandate that all county clerks issue marriage licences," said the statement by Liberty Counsel, which is representing Davis.

The same injunction request was denied last month by U.S. District Judge David Bunning, who jailed Davis on Thursday.

Charla Bansley, communications director for Liberty Counsel, said Davis could be released from jail immediately if the motion were granted by the U.S. Court of Appeals for the Sixth Circuit ordering Beshear to issue Davis an "accommodation" — allowing her to remove her name and title from official marriage certificates issued in Rowan County.

By doing that, Davis would not be sanctioning any same-sex unions and her conscience would be satisfied, they say.

"If there was an accommodation, she would be released [from jail] because she would no longer be in contempt," Bansley said.

On Sunday, about 30 protesters lined the sidewalk outside Bunning's home in Fort Thomas, Kentucky, carrying signs that read "Free Kim Davis."

Davis, an apostolic Christian, says it would be a sin for her to issue a marriage licence to a same-sex couple because the licences are issued under her authority. She tried in vain to have state lawmakers change the law as a legal challenge to Kentucky's same-sex marriage ban wound its way through the federal appeals court.

Davis stopped issuing all marriage licences in June the day after the U.S. Supreme Court legalized same-sex marriage nationwide. Two gay couples and two straight couples sued her. Bunning ordered Davis to issue the licences and the Supreme Court upheld his ruling by refusing to hear her appeal.

But Davis still refused to do it, saying she could not betray her conscience or her God.

On Thursday, Bunning ruled Davis was in contempt of court for disobeying his order and sent her to jail. Her deputy clerks then issued marriage licences to gay couples Friday with Davis behind bars.

Bunning indicated Davis will be in jail at least a week. She could stay longer if she continues to not obey the judge's order. Bunning had offered to release Davis from jail if she promised not to interfere with her deputy clerks as they issued the licences, but Davis refused.

Kentucky law requires marriage licences be issued under the authority of the elected county clerk. Davis views issuing marriage licences to same-sex couples as a stamp of approval of something she believes is a sin. She has said she will not issue marriage licences until the state legislature changes the law so the licences can be issued under someone else's authority.

The state legislature is not scheduled to meet again until January and Beshear has refused to call a special session. Davis has refused to resign her $80,000-a-year job. As an elected official the only way she could lose her job is to lose an election or have the state legislature impeach her, which is unlikely given its conservative nature.