(CBS/AP) The Supreme Court on Thursday rejected integration plans in two major public school districts but left the door open for using race to assign students in limited circumstances.

The decision in cases affecting schools in Louisville, Ky., and Seattle could imperil similar plans in hundreds of districts nationwide, and it further restricts how public school systems may attain racial diversity.

The court split, 5-4, with Chief Justice John Roberts announcing the court's judgment. The court's four liberal justices dissented.

In his ruling, Roberts took aim at the way Seattle assigns students to schools after classifying them as "white" or "non white" and the way Louisville labels students as "black" or "other," reports CBS News correspondent Wyatt Andrews .

"The way to stop discrimination on the basis of race is to stop discriminating on the basis of race," Roberts said.

Yet Justice Anthony Kennedy would not go as far as the other four conservative justices, saying in a concurring opinion that race may be a component of school plans designed to achieve diversity.

To the extent that Roberts' opinion could be interpreted to foreclose the use of race in any circumstance, Kennedy said, "I disagree with that reasoning."

"A district may consider it a compelling interest to achieve a diverse student population," Kennedy said. "Race may be one component of that diversity."

He agreed with Roberts that the plans in Louisville and Seattle violated constitutional guarantees of equal protection.

"These plans in these districts are finished, but Justice Kennedy may have saved slightly different plans in other school districts around the country because in his concurring opinion he says you can't always and forever rule out the use of race as a factor," CBS News legal analyst Andrew Cohen says.

"This is not the crushing blow to affirmative action in public schools that it initially appears to be," Cohen says.

Justice Stephen Breyer, in a dissent joined by the other liberals on the court, said Roberts' opinion undermined the promise of integrated schools that the court laid out 53 years ago in its landmark decision in Brown v. Board of Education.

"To invalidate the plans under review is to threaten the promise of Brown," Breyer said.

While Roberts said the court was being faithful to the Brown decision, Justice John Paul Stevens in a separate dissent called the chief justice's reliance on Brown to rule against integration "a cruel irony."

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