Oklahoma state representatives voted overwhelmingly on Thursday to advance a bill that would provide immunity from lawsuits to clergy who refuse to conduct marriages for same-sex couples.

The bill, approved by 88-7 in the state House of Representatives, would protect clergy members from any civil claim or cause of action if they refuse to preside over or recognise a marriage of same-sex couples because of their conscience or religious beliefs. The measure next goes to the state Senate for consideration.

The bill's sponsor, Republican Representative David Brumbaugh, said many pastors asked for the legislation after a federal judge overturned Oklahoma's ban on gay marriage in January 2014.

The ministers are concerned about being sued under public accommodation laws if they turn away same-sex couples who want to marry, he said.

"It's not about discrimination or anything like that, it's just that we want to make sure they were protected," Brumbaugh said.

Brumbaugh said he was not sure if any states had approved similar bills.

The bill is one of several proposals before the Republican-dominated Oklahoma Legislature intended to protect the interests of people who object to the lifting of the gay marriage ban.

Gay rights supporters have said they would challenge the proposed measures in court if they become law.

Meanwhile in Alabama, a federal judge on Thursday ordered an  official to start issuing marriage licences to gay couples in compliance with an earlier order, but couples in most counties were still unable to obtain licenses.

US District Judge Callie Granade's order clarified that Mobile County Probate Court Judge Don Davis was compelled to adhere to her previous ruling striking down the state's gay marriage ban despite a contravening order from Alabama Supreme Court Justice Roy Moore that led many state judges to refrain from issuing licences to gay couples.

Granade's directive marked the latest twist in the controversy over gay marriage in Alabama, where probate judges have faced conflicting orders from federal and state courts. The resulting disarray has allowed same-sex couples to marry in places such as Birmingham, while those applying for marriage licenses in dozens of counties have been turned away.

Alabama is the 37th US state where gay marriage has been legalised, and the first in the Deep South, where many voters are socially conservative.

The US Supreme Court refused on Monday to grant a request from Alabama's Republican attorney general to keep the weddings on hold until it decides later this year whether laws banning gay matrimony violate the US Constitution.

But Moore ordered state judges to defy Granade's ruling and uphold the state's gay marriage ban, an order his office said remained in effect despite the Supreme Court's action.

Granade's order on Thursday applied specifically to Mobile County, where, within an hour of the ruling, same-sex couples who had been waiting in line at a county building began to receive licences.