The Obama administration urged the Supreme Court on Monday to continue to allow universities to take race into account when assembling their student bodies, saying the government has a “vital interest” in drawing its leaders from a diverse pool of college graduates.

The administration supported the University of Texas, whose policy of considering race as one factor in deciding who will be admitted to the flagship university in Austin is being challenged.

The case will be one of the most important of the court’s coming term — underscored by more than 50 friend-of-the-court briefs filed by outside groups and individuals.

The Supreme Court said nine years ago that universities had a legitimate interest in building diverse classes and provided guidelines for administrators: An applicant’s status could not be automatically boosted because of his or her race, but race could be one factor in a holistic review of the person’s qualifications.

Opponents of affirmative action have urged the court — now with justices more averse to race-conscious solutions — to reconsider the 2009 decision in Grutter v. Bollinger, or at least to find that UT’s process falls outside those strict standards.

The policy is being challenged by a white student, Abigail Fisher, who said she was rejected by the university while less-qualified minorities were admitted, violating her constitutional rights. She graduated from Louisiana State University in the spring.

The administration’s brief was submitted by Solicitor General Donald B. Verrilli Jr., and reflected the positions of the departments of Defense, Health and Human Services, Commerce, Education, and Labor.

The government “has a vital interest in drawing its personnel — many of whom will eventually become its civilian and military leaders — from a well-qualified and diverse pool of university and service-academy graduates of all backgrounds who possess the understanding of diversity that is necessary to govern and defend the United States,” Verrilli wrote.

Fisher’s attorneys, who filed their brief to the court in May, argued that “if any state action should respect racial equality, it is university admission. Selecting those who will benefit from the limited places available at universities has enormous consequences for the future of American students and the perceived fairness of government action.”

UT has a unique system, admitting all Texas students who finish in the top 10 percent of their high school classes. That accounts for about 75 percent of its freshman class.

For out-of-state students and those such as Fisher who do not make that cut, applicants are ranked by grades, test scores and other factors, including leadership qualities and work experience. Race is also considered.

Fisher’s attorneys argued that the top-10 approach already has increased the university’s diversity and that the race-conscious approach is unnecessary. The university contends that its number of Hispanic and African American students is too low to be representative of a state that will soon have no majority race.

The plan was upheld by the U.S. Court of Appeals for the 5th Circuit, but dissenting judges urged the Supreme Court to review it.

The court’s new membership presents a formidable obstacle for supporters of affirmative action. Justice Sandra Day O’Connor, who wrote the 5-4 majority opinion in Grutter, has been replaced by Justice Samuel A. Alito Jr., who has voted against race-based government programs and remedies.

The court’s newest member, Justice Elena Kagan, has recused herself from the case, presumably because she worked on it in her previous role as solicitor general. That means it will be heard by an eight-member court, and a tie would affirm the appeals court decision upholding the policy.

The case is Fisher v. University of Texas .