WASHINGTON — Courts must take a skeptical look at affirmative-action programs at public colleges and universities, the Supreme Court ruled Monday, in a decision that is likely to set off a wave of challenges to race-conscious admissions policies nationwide.

The 7-to-1 decision avoided giving a direct answer about the constitutionality of the program, used by the University of Texas at Austin, that was before the court.

The program will continue for now, but the justices ordered an appeals court to reconsider the case under a demanding standard that appears to jeopardize the program.

The ruling was simultaneously modest and significant, and its recalibration of how courts review the constitutionality of race-conscious decisions by the government will reverberate beyond higher education.