The court heard arguments in a challenge to the program from a white Texan who contends she was discriminated against when the university did not offer her a spot in 2008.

The court’s conservatives cast doubt on the program that uses race as one among many factors in admitting about a quarter of the university’s incoming freshmen class.

Justice Anthony Kennedy, whose vote could be decisive, looked skeptically on Texas’ defense of the program. “What you’re saying is what counts is race above all,” Kennedy said.

Opponents of affirmative action say the university is practicing illegal discrimination by considering race at all. The case, one of the most watched in the court’s current term, focuses new attention on the constitutionality of racial preferences in admission decisions by public universities.

Twenty-two-year-old Abigail Fisher, who was denied admission, was among the hundreds of spectators at the arguments. Also in attendance was retired Justice Sandra Day O’Connor, who wrote the majority opinion in a 2003 case that upheld the use of race in college admissions.

Justice Samuel Alito, O’Connor’s successor, has voted consistently against racial preferences since he joined the court in 2006 and appears likely to side with Fisher.

Among the liberal justices who looked more favorably on the Texas admissions system was Justice Sonia Sotomayor. She told Bert Rein, Fisher’s Washington-based lawyer, that he was looking to “gut” the nine-year-old decision.

The federal appeals court in New Orleans upheld the Texas program, saying it was consistent with the 2003 decision in Grutter v. Bollinger.

Chief Justice John Roberts, Justice Antonin Scalia and Alito, all conservatives, raised repeated objections to the affirmative action plan.

Roberts wanted to know how the university would determine when it had a “critical mass” of diversity on campus that would allow it to end the program.

Near the end of the session, he complained, “I’m hearing a lot about what it’s not. I would like to know what it is.”

The university says the program is necessary to provide the kind of diverse educational experience the high court has previously endorsed. The rest of its slots go to students who are admitted based on their high school class rank, without regard to race

Opponents of the program say the university is practicing illegal discrimination by considering race at all, especially since it achieves significant diversity through its race-blind admissions.

After the argument concluded, Fisher read a brief statement outside in which she said she hoped the court would rule that race or ethnicity “should not be considered when applying to the University of Texas.”

Justice Elena Kagan is not taking part in the case, probably because she worked on it at the Justice Department before joining the court.

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Associated Press writer Jesse J. Holland contributed to this report.