Groups opposed to the affirmative action policies at the University of Texas at Austin were given permission by the Supreme Court last week to challenge the institution's right to discriminate in favour of ethnic-minority students.
This right was affirmed by a Supreme Court case in 2003 involving the University of Michigan, but Texas has overstepped the remit of the original ruling, plaintiffs claim.
The plaintiffs, who include pressure groups, private individuals and charities, argue that Texas already admits a high number of black and Hispanic students through a statewide "10 per cent" plan - in which students in the top 10 per cent of their high school's graduating class are automatically admitted to the public university of their choice.
The scheme's success eliminates the need for race-based policies, the plaintiffs claim.
But Bill Powers, Austin's president, said the flexibility to consider each applicant's experiences and background was important to "provide the best environment in which to educate and train" students.
Civil rights leader Jesse Jackson has also backed the university, saying that black and Hispanic students remain at a disadvantage due to social inequalities in the US.
But Stephen Balch, chair of the National Association of Scholars, an anti-affirmative action group, argued that an end to race-based discrimination was "the only way to usher in true racial equality" and that there were many "race-neutral ways" to promote equality.
A lawsuit over Texas' affirmative action policies was rejected by a federal district court and an appeal court in 2008, but the latest challenge has a greater chance of success.
The Michigan decision was narrowly decided by five votes to four and the author of the 2003 judgment, Justice Sandra Day O'Connor, has since left the Supreme Court.
Another likely supporter of affirmative action, Justice Elena Kagan, did not take part in the court's decision to hear the appeal and her links to the university mean she is not expected to take part in the review.