WASHINGTON—The Supreme Court on Tuesday upheld Michigan's decision to end affirmative action at its public universities in a 6-2 ruling, but the justices were divided in their reasoning, suggesting continued uncertainty over the broader issue of racial preferences.

The ruling leaves in place a 2006 Michigan ballot initiative where voters ended race-based admissions at state schools, and means racial preferences won't soon return to the University of Michigan—or any other public university in states that have chosen to end...