The case is being appealed.
Other states that joined the brief against gay marriage are Alabama, Florida, Indiana, Louisiana, Michigan, South Carolina and Virginia, according to the Casper Star-Tribune. The states argue that same-sex marriage is not a fundamental right.
"If public affirmation of anyone and everyone's personal love and commitment is the single purpose of marriage, a limitless number of rights claims could be set up that evacuate the term marriage of any meaning," the brief said.
Former Utah Sen. Scott McCoy, the first openly gay state senator, said Saturday he is not surprised Utah signed on to the opposition brief. If the California ruling against Proposition 8 is upheld, it would follow that Utah's Amendment 3, which defines marriage as a union exclusively between a man and a woman, is unconstitutional, he said.
States can't keep people from marrying based on race or religion, McCoy said, and they shouldn't be able to do it based on sexual orientation.
The amicus brief was criticized by Jason Marsden, of the Matthew Shepard Foundation, a Denver-based gay-rights organization. He said it was "very puzzling" that Wyoming Attorney General Bruce Salzburg joined, given that the Wyoming Legislature last year defeated a resolution to ban recognition of gay marriages performed in other states.
"I thought it'd be pretty clear that the legislative branch, at least, doesn't want to send this kind of message of lack of acceptance to its gay and lesbian citizens," Marsden said. "But the attorney general appears to have taken another direction."
Salzburg, who was away from his office Friday, wasn't available for comment.
Becky Vandeberghe, of WyWatch Family Action, a Wyoming-based family-values group that opposes gay marriage, said she was "very pleased" to see that Wyoming joined the brief. WyWatch joined more than 30 other groups in submitting an amicus brief of their own to the 9th Circuit Court of Appeals last week opposing the California decision.
"The California voters spoke, and that should be honored," Vandeberghe said. "We don't believe that judges should be overruling what the will of the people is."
Salt Lake Tribune staff contributed to this report.