Mr Powell, the highest-ranking black American in the cabinet, said in a television interview that while he believes President Bush is "committed to diversity" he took a different view.
His statement also put him at odds with the administration's other high-profile black official, the national security adviser, Condoleezza Rice.
The row centres on the admissions policy of the University of Michigan, which awards extra points to black, hispanic and native American candidates in its scoring system for entry, to ensure racial diversity.
White students have claimed that the policy unfairly discriminates against them and is unconstitutional.
On Sunday, Mr Powell said: "Whereas I have expressed my support for the policies used by the University of Michigan, the president, in looking at it, came to the conclusion that it was consitutionally flawed, based on legal advice he received."
Last week, the White House filed papers with the supreme court urging the judges to find against the university. Mr Bush also spoke out against college admissions policies that "unfairly reward or penalise prospective students based solely on their race.
Over the weekend, Ms Rice backed the president, while insisting that she believes race can and should be a factor in admissions policies, acknowledging that she herself had been a beneficiray of such a system at Stanford.
"[Mr Bush] has made a case that race-neutral means ought to be tried first. And he has, as president, appropriately left to the court the question of what the limits of the constitution are in pursuit of diversity. And I think that's the appropriate place for the president to be," Ms Rice said.
It is a contentious issue for the Republican administration which is anxious about alienating black and hispanic voters, some 90% of whom back the Democrats, particularly coming so soon after the controversy surrounding remarks made by Trent Lott.
Mr Lott, the former Senate leader, was forced to resign after he said that America would have been a better place if a segregationist had won the presidency in 1948.
In an era of otherwise swingeing budget cuts, Mr Bush chose yesterday, the public holiday held in honour of Martin Luther King, to annouce a 5% rise in grants to historically black colleges and to those where at least 25% of the students are hispanic.
Mr Powell was eager to point out that while he may differ with Mr Bush on this particular issue, he believes the president is committed to addressing the underlying issues of racial injustice.
"I do know that he is absolutely committed to diversity, and the manner in which the brief has been filed to the court allows the court to makes its choice on the Michigan case, but doesn't go to the underlying issues."