Wyoming Governor Matt Mead, a Republican, on Thursday said he does not believe the state should appeal an upcoming ruling challenging the constitutionality of the state's ban on gay marriage.

As part of the Tenth Circuit, Wyoming is affected by a federal appeals court's ruling striking down similar bans in Utah and Oklahoma. The court's rulings took effect last week after the Supreme Court refused to hear appeals in the cases.

(Related: Gay marriage fights move to South Carolina, Wyoming, Arizona, Montana, Kansas.)

At a hearing on Thursday, the National Center for Lesbian Rights (NCLR) and Wyoming Equality asked U.S. District Judge Scott W. Skavdahl to force Wyoming officials to comply with the rulings.

Skavdahl said he would issue a ruling before 5 PM on Monday.

Mead, who is seeking re-election, was asked about the possibility of an appeal during a televised debate.

“The answer is no, we shouldn't appeal the ruling,” Mead answered.