Supporters of the tests say they provide a uniform way of judging students from different schools and backgrounds, but should not be used alone.

The litigation comes as the University of California system is already embroiled in a debate over whether to continue using the tests to judge about 200,000 high school students who apply to its nine undergraduate schools each year. A work group is currently studying whether the ACT and SAT should be a required element for admission; its report is due next year.

More than 1,000 colleges and universities across the country have already made standardized test scores optional, according to FairTest, an advocacy group that wants to do away with the tests and that consulted on the litigation.

The University of Chicago, a top-ranked school, announced last year that it was going test-optional. This fall it reported that as a result of the new policy, along with more financial aid, outreach and mentoring, the entering class of 2019-20 had 24 percent more first-generation and low-income students and 56 percent more rural students than the previous year. About 10 percent of applicants did not submit test scores, a spokesman said.

But the plaintiffs are seeking to go beyond test-optional policies and to bar students from submitting test scores even if they want to, according to Mr. Rosenbaum.