The governor in a court filing on Tuesday took no position on whether the ban, enacted by voters in November as Proposition 8, is constitutional.
But he said the lawsuit filed last month by two same-sex couples presents important legal issues "that require and warrant judicial determination." The governor also urged U.S. District Judge Vaughn Walker to decide the case quickly.
Walker is scheduled to hold a hearing July 2 on the couples' bid for a preliminary injunction blocking implementation of Proposition 8.
The lawsuit was filed the day after the California Supreme Court upheld Proposition 8 on May 26. The couples claim the ban on same-sex marriage violates their federal constitutional rights to due process and equal treatment.
For procedural reasons, the governor and other state officials are named as defendants in the lawsuit. But the main task of defending Proposition 8 is expected to be carried out by the sponsors of the initiative.
They filed a brief last week saying that "nothing in the Constitution requires such a radical redefinition of the ancient institution of marriage."
California Attorney General Jerry Brown, who is also a defendant in the lawsuit, said in a response brief last week that he believes the ban violates the federal Constitution because "it cannot be squared" with the 14th Amendment guarantee of equal treatment.
But both Brown and Schwarzenegger urged Walker to hold off on issuing a preliminary injunction and to wait until he reaches a final judgment in the case before issuing any orders.
They said a preliminary injunction before there is a final resolution of the case could create public uncertainty and "legal limbo."
The federal lawsuit was filed by Kris Perry and Sandy Stier of Berkeley and Paul Katami and Jeff Zarrillo of Burbank. Both couples say they want to marry, but were denied marriage licenses by their county clerks' offices because of Proposition 8.
Their lawyers are prominent attorneys Theodore Olson of Washington, D.C., and David Boies of Armonk, N.Y., who argued on opposite sides of the Bush v. Gore case that decided the 2000 presidential election.
Proposition 8, enacted as a state constitutional amendment, overturned a May 2008 decision in which the California Supreme Court said the state constitution provided a right to same-sex marriage.
The court upheld the ballot measure on May 26 as being within voters' initiative power. At the same time, however, the court said that 18,000 gay and lesbian marriages performed before the Nov. 4 election will remain valid.