WASHINGTON — Supreme Court justices indicated Tuesday that they are poised to deliver a fresh blow to affirmative action, hinting they will uphold a voter-approved ban on racial preferences at Michigan’s state-run universities.
Hearing arguments in Washington, the court’s Republican-appointed justices suggested they saw the measure as a legitimate ban on racial discrimination. A federal appeals court said the opposite, ruling that the affirmative action ban unconstitutionally stripped racial minorities of their rights.
‘‘Is it unreasonable for the state to say, ‘Look, race is a lightning rod’?’’ Chief Justice John Roberts said. He asked why a state couldn’t take racial classifications ‘‘off the table’’ and try to achieve diversity through other means.
A decision backing the initiative would have symbolic as well as substantive importance. A decade ago the University of Michigan won a Supreme Court decision that let institutions across the country continue to use race as one factor in the admissions process.
Three years later, the Michigan ballot initiative amended the state constitution to block such use at state schools, nullifying the Supreme Court decision for the very university that secured it. Black enrollment is down about 30 percent at the undergraduate and law schools since the measure took effect, according to university figures.
Justice Sonia Sotomayor, the court’s lone Hispanic, said that one of the sponsors of the measure had said the goal was to ‘‘bring back’’ segregation. ‘‘And it appears to have done just that,’’ she said.
As the justices heard arguments, about 200 affirmative action supporters gathered on the sidewalk in front of the court building, displaying signs and listening to speakers. Most members of the group were college-age or younger.
Justice Elena Kagan has recused herself from the case. She was President Obama’s solicitor general when the administration had a chance to get involved in the litigation.
Roberts has sought to steer the court toward a color-blind approach to the Constitution. The justices last year overturned a core part of the Voting Rights Act, the law designed to protect minorities at the polls. The court also issued a compromise ruling that ordered tougher judicial scrutiny of university affirmative action programs.
The latest case involves different legal issues from those in past affirmative action disputes. Rather than debating whether universities violate the rights of white students with affirmative action programs, the court is considering whether state bans on racial preferences amount to discrimination against minorities.
Michigan is one of 10 states where race-conscious admissions are barred as a matter of law.
A federal appeals court said the Michigan measure put racial minorities at a unique disadvantage. The 8-7 decision said minorities are barred from asking universities for special preferences — something athletes, band members, and children of alumni could still do.
The measure ‘‘singles out race for different treatment,’’ Mark Rosenbaum, a lawyer with the American Civil Liberties Union arguing against the law, said Tuesday.
That position gained little traction among court conservatives. Justice Anthony Kennedy, usually the swing vote on issues involving race, questioned the limits of Rosenbaum’s argument. Kennedy asked whether the state legislature, a state executive department, or a university president could bar the use of race in admissions. Roberts and Justice Samuel Alito asked similar questions.
‘‘At what point is it that your objection takes force?’’ Kennedy asked.
The court will rule by July in the case.