A U.S. federal judge has rejected arguments that the judge who overturned California's ban on gay marriage was biased.

Chief U.S. District Judge James Ware ruled Tuesday Judge Vaughn Walker did not have to reveal that he, himself, was in a same-sex relationship.

Lawyers for those in favor of the gay marriage ban argued the judge should have been disqualified or recused himself from the case because his long-term relationship meant he could have had a personal interest in allowing same-sex marriages.

Walker publicly revealed the relationship after he retired in February.

In his ruling Tuesday, Judge Ware said the U.S. law does not require a judge to step down simply because he could be affected by the verdict in the same way as other members of the general public.

California's Supreme Court legalized same-sex marriages in 2008, but just months later voters banned the unions. They narrowly approved a measure known as Proposition 8, which defines marriage as the union between a man and a woman.

Last year, Walker struck down Proposition 8, saying the ban prevents the state from fulfilling its constitutional obligation to provide marriages on an equal basis.

Walker's decision on the constitutionality of the ban has been appealed.