WASHINGTON — The Supreme Court agreed on Monday to take a second look at the use of race in admissions decisions by the University of Texas at Austin, reviving a potent challenge to affirmative action in higher education.

The move, which supporters of race-conscious admissions programs called baffling and ominous, signaled that the court may limit or even end such affirmative action. The advocates speculated that the court’s most conservative members had cast the four votes needed to grant review of the case in the hope that Justice Anthony M. Kennedy would supply the fifth vote to strike down the Texas admissions plan.

Justice Kennedy has never voted to uphold an affirmative action program.

The consequences would be striking if the court sided with the plaintiff in the case, a white woman named Abigail Fisher, and did away with racial preferences in higher education. It would, all sides agree, reduce the number of black and Latino students at nearly every selective college and graduate school, with more Asian-American and white students gaining entrance instead.

“Over the last few days, liberals have been celebrating a string of important victories involving health care and same-sex marriage,” said Justin Driver, a law professor at the University of Chicago. “But liberals have also been bracing themselves for the other shoe to drop. This decision to grant review means, at a minimum, that the other shoe will remain suspended in midair for the next several months.”