Proposition 8, the ban on gay and lesbian marriages, was passed by California voters last November as an amendment to the state Constitution.
A lawsuit challenging the initiative was filed by in federal court in May by two same-sex couples who say the measure violates their federal constitutional rights to due process and equal treatment.
In the motion to be argued before U.S. District Judge Vaughn Walker, the sponsors of Proposition 8 say a trial on the lawsuit isn't needed because "there is no fundamental right to same-sex marriage" in the U.S. Constitution.
Their lawyers have argued in court papers that marriage between a man and a woman "is one of the central institutions of our society" and that same-sex marriage is "a radical and highly controversial experiment."
If the lawsuit is not dismissed, it is scheduled for a trial before Walker in January.
Lawyers for the two couples challenging the measure say there should be a full trial to allow them to present evidence on their arguments that Proposition 8 was passed with discriminatory intent and that there is no rational basis for the measure.