(Reuters) - The U.S. Supreme Court on Tuesday dealt a blow to the use of racial preferences in higher education by upholding a Michigan law that bans the practice in state university admissions.

In a 6-2 vote, the court rejected a challenge to the voter-approved ban, although the justices were divided as to the legal rationale. The court made it clear it was not deciding the larger and divisive question of whether affirmative action admission policies can be lawful.

The majority opinion rejected the argument made by civil right groups that the 2006 Michigan constitutional amendment that passed as a ballot initiative to ban the practice had imposed burdens on racial minorities in violation of the U.S. Constitution's guarantee of equal protection.

Affirmative action programs, first advocated in the 1960s to combat discrimination against racial minorities, have faced a backlash from conservatives in recent decades. Court rulings and action by states have chipped away at the practice.

Michigan is one of eight states to ban affirmative action. The others are Arizona, California, Florida, Nebraska, New Hampshire, Oklahoma and Washington.

In November 2012, a divided 6th U.S. Circuit Court of Appeals in Cincinnati ruled Michigan's ban unconstitutional, prompting the state to appeal to the Supreme Court.

On Tuesday, the justices in the majority were divided three ways.

Justice Anthony Kennedy wrote an opinion, joined by Chief Justice John Roberts and Justice Samuel Alito, saying that the appeals court that threw out the law did not have the authority to do so.

"This case is not about how the debate about racial preferences should be resolved," Kennedy wrote. "It is about who may resolve it."

The dissenting votes came from two of the liberal members of the court, Justice Sonia Sotomayor and Justice Ruth Bader Ginsburg.

Sotomayor read parts of the dissent from the bench. She wrote that the decision was a blow to "historically marginalized groups, which rely on the federal courts to protect their constitutional rights."

The court had undermined its own precedents, which state that the majority cannot suppress minorities' right to participate in the political process, Sotomayor said.

Justice Antonin Scalia wrote a separate opinion, joined by Justice Clarence Thomas, in which he said that challenges to laws that rest on equal protection claims must show that the law reflects a discriminatory purpose. The Michigan law did not, he said.

Justice Stephen Breyer was the only member of the liberal wing of the court to join the majority. He wrote that the ban was constitutional because the prohibition moved the decision on whether to adopt race-conscious admissions policies from university officials to the voters.

Justice Elena Kagan did not take part, presumably because she worked on the case while in her previous position as United States solicitor general.

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