SAN FRANCISCO—Supporters of California's Proposition 8, which bans gay marriage, filed a motion Monday seeking to reinstate the law because the judge who overturned the ban recently disclosed he is gay and in a relationship.

In a brief filed with the Ninth Circuit Court of Appeals, lawyers for a group defending Proposition 8 called ProtectMarriage.com argued that U.S. District Judge Vaughn Walker failed to disclose before the trial his own 10-year same-sex relationship and should have recused himself from the case.

Andy...