Opponents have criticised a US Supreme Court ruling that says race cannot be used as a factor in school entry.
Schools in Seattle are no longer able to impose racial quotas
Democratic presidential candidates spoke out against the court's 5-4 judgement, with Senator Barack Obama describing it as "wrong-headed".
But others backed the court, saying the social landscape in the US had changed since a landmark Supreme Court desegregation ruling in 1954.
Estimates suggest one in 15 US school boards may now change entry policies.
Thursday's narrow ruling was the first time since 2003 that the Supreme Court had ruled on the issue of race and education - one of the most emotive issues in the US.
The make-up of the court has changed since then, with moderate judge Sandra Day O'Connor replaced by a more conservative justice, Samuel Alito.
The new ruling struck down school entry policies in Seattle and in Louisville, Kentucky, following protests from white parents whose children had been denied entry to schools because they would have exceeded a quota of non-black pupils.
Many US schools adopted so-called "affirmative action" programmes during the civil rights era as a means of desegregating racially-divided schools.
They are no longer compulsory, but hundreds of school districts have kept them in place on a voluntary basis.
The BBC's James Westhead, in Washington, says the new verdict is being seen as one of the Supreme Court's most far-reaching and controversial rulings on race.
However, he notes that the court was sharply divided, with four dissenting justices publishing a counter-opinion. One of those in favour also released comments qualifying his decision.
The only black justice, Clarence Thomas, voted with the majority.
Speaking at a presidential debate hours after the ruling, leading Democrats criticised the court.
"Once again, the [Chief Justice John] Roberts court has shown its willingness to erode core constitutional guarantees," said Senator Hillary Clinton.
Mr Obama, hoping to become the first black US president, said the 1954 Brown vs Board of Education ruling that outlawed segregation in schools was the reason he had succeeded in public life.
In his ruling, Chief Justice Roberts suggested that racial classifications perpetuated the very divisions they were put in place to dissolve.
"The way to stop discrimination on the basis of race is to stop discriminating on the basis of race," he added.
Splits among civil rights advocacy groups and academics hinted at the complexity of the issue.
The Supreme Court is the guardian of the US constitution
The American Civil Liberties Union, one of the largest advocacy groups, said it had mixed feelings.
The organisation said the verdict was a "significant step backwards", but pointed to comments by Justice Antony Kennedy, who voted in favour but said he did not oppose efforts to end segregation as a matter of principle.
Correspondents say Justice Kennedy's opinion may prevent the judgement being used as a precedent for similar rulings on a nationwide basis.
But Jennifer Gratz, of the American Civil Rights Institute, a separate group, told the BBC that the Supreme Court had made a wise decision.
"It's about time that the [Supreme] Court got in line with the constitution and the American people's belief that race should not be a factor to our government," she said.