Powell, one of two black members of Mr. Bush's Cabinet, said he supports methods the University of Michigan uses to bolster minority enrollments in its undergraduate and law school programs. The policies offer points to minority applicants and set goals for minority admissions.
"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 constitutionally flawed based on the legal advice he received," Powell said on CBS News' "Face the Nation."
It was a rare public acknowledgment of dissent with the president and with other top White House aides.
National security adviser Condoleezza Rice said she backed Mr. Bush's decision to step into the case before the Supreme Court and to argue that the University of Michigan's methods were unconstitutional. She said on NBC's Meet the Press Sunday that there are "problems" with the university's selection policies, and cited the points system.
But she also said race can be a factor in colleges' selection process. The brief the Bush administration filed with the Supreme Court was silent on that issue of whether race can be a factor under some circumstances. It also does not ask the court to overturn the 1978 Bakke decision that found racial preferences are not unconstitutional.
"It is important to take race into consideration if you must, if race-neutral means do not work," she said.
Rice said she had benefited from affirmative action during her career at Stanford University.
"I think they saw a person that they thought had potential, and yes, I think they were looking to diversify the faculty," she said.
"I think there's nothing wrong with that in the United States," Rice said. "It does not mean that one has to go to people of lower quality. Race is a factor in our society."
In a Friday interview with the American Urban Radio Network, Rice said she agreed that affirmative action is needed "if it does not lead to quotas."
In a speech to the Republican National Convention in 2000, Powell sharply criticized GOP attacks on affirmative action.
"We must understand the cynicism that exists in the black community," he said. "The kind of cynicism that is created when, for example, some in our party miss no opportunity to roundly and loudly condemn affirmative action that helped a few thousand black kids get an education, but you hardly heard a whimper from them over affirmative action for lobbyists who load our federal tax codes with preferences for special interests."
Sunday on CNN, Powell said he remained "a strong proponent of affirmative action."
Education Secretary Rod Paige is the other black member of Bush's Cabinet. As national security adviser, Rice is not a Cabinet member.
Paige firmly agrees with Mr. Bush's stance, a spokesman said Sunday.
"Secretary Paige believes in equal opportunity for all students and he fully supports President Bush's position on the University of Michigan case," said spokesman Dan Langan. He wasn't sure whether Paige agreed with Rice that race can sometimes be a factor in university admissions.
In an unusual Sunday night announcement, the White House said Mr. Bush's budget proposal for the upcoming fiscal year would increase funding by 5 percent for grants to historically black colleges, universities, graduate programs and Hispanic education institutions.
The money affects three programs.
The Historically Black Colleges and Universities program makes grants to 99 eligible institutions to help strengthen infrastructure and achieve greater financial stability.
The Historically Black Graduate Institutions program makes 5-year grants to 18 institutions to expand capacity for providing graduate-level education.
The Hispanic-Serving Institutions program makes grants of up to five years to eligible institutions — those with a full-time population of at least 25 percent Hispanic students, at least 50 percent of which are low-income.
In its brief to the Supreme Court, the administration argued that policies at the University of Michigan and its law school fail the constitutional test of equal protection for all under the law, and ignore race-neutral alternatives that could boost minority presence on campuses.
A White House spokesman declined to say Sunday night why the black and Hispanic grant programs are acceptable, when the University of Michigan admission system is not.
Mr. Bush, who drew 9 percent of the black vote in 2000, was attending a predominantly black church on the Martin Luther King Jr. holiday Monday.