The justices said they will hear for a second time the case of a white woman who was denied admission to the university's flagship Austin campus.
The conservative-leaning federal appeals court in New Orleans has twice upheld the university's admissions process, including in a ruling last year that followed a Supreme Court order to reconsider the woman's case.
The case began in 2008 when Abigail Fisher, who is white, was denied admission to the University of Texas's flagship Austin campus because she did not graduate in the top 10 per cent of her high school class — the criterion for 75 per cent of the school's admissions. The university also passed her over for a position among the remaining 25 per cent, which is reserved for special scholarships and people who meet a formula for personal achievement that includes race as a factor.
Edward Blum, who helped engineer Fisher's lawsuit, said he is encouraged by the court's second look at the case. "The outcome of this case may bring our nation closer to the day when a student's race and ethnicity is not a factor that a school may consider during the admissions process," Blum said.
University of Texas president Greg Fenves defended the school's admissions policy as narrowly-tailored and constitutional. Fenves said the use of race "as one factor in an individualized, holistic admissions policy allows us to assemble a student body that brings with it the educational benefits of diversity for all students."
The case went to the U.S. Supreme Court in June 2013. But rather than issue a definitive ruling on affirmative action, the justices voted 7-1 to tell a lower appeals court to take another look at Fisher's lawsuit. That meant the university's admissions policies remained unchanged.
Last year, the 5th U.S. Circuit Court of Appeals again upheld the university's admissions policy. Fisher is a graduate of Louisiana State University.
Justice Elena Kagan is not taking part in the case. She sat out the first round as well, presumably because of her work on the case when she served in the Justice Department before joining the court.
The case, Fisher v. University of Texas, 14-981, will be argued in the fall.
Associated Press writer Jim Vertuno contributed to this report from Austin, Texas.