Gov. Arnold Schwarzenegger said in a court filing that Proposition 8 “presents important constitutional questions that require and warrant judicial determination.”

His statement came as part of a response to the Ted Olson-David Boies filing of a suit challenging the constitutionality of California’s same-sex marriage ban. The suit is backed by the American Foundation for Equal Rights, led by political consultant Chad Griffin and including a board made up of entertainment industry figures such as Rob Reiner, Bruce Cohen and Dustin Lance Black.

Schwarzenegger’s filing was required as he is named as a defendant in the suit. It put him in the position of issuing some kind of defense of a law that he opposed during the election.

Attorney General Jerry Brown also was named in the suit, and he issued a brief last week that was stronger in suggesting that the law was unconstitutional.

Schwarzenegger’s filing also said, “The administration encourages the court to resolve the merits of this action expeditiously.”

The first hearing on the suilt will be held on July 2 at U.S. District Court in San Francisco. Schwarzenegger and Brown issued separate filings opposing Boies and Olson’s request for an injuction to put Prop 8 on hold until the case is resolved.

In a statement, Griffin said that they “are extremely pleased Gov, Schwarzenegger does not dispute the unconstitutionality of Proposition 8 and agrees that swift action is needed to ensure that every person is treated equally under the law.”

Andrew Pugno, general counsel of Protect Marriage, which ran the Yes on 8 campaign, has said the suit “has very little chance of succeeding” and that they plan a “vigorous defense” of the law.