In sidestepping the issue, Mr. Bush said it is up to the high court to "define the outer limits of the Constitution" without his input.
The Supreme Court announced Tuesday that it will hear oral arguments on the University of Michigan policies on April 1. The court will hear two cases back to back that day, one challenging the school's undergraduate admissions program and another challenging a slightly different program at the university's law school.
Mr. Bush declared last week that Michigan admissions policies are unconstitutional because of their use of what he said were racial quotas. But he skirted the larger question of whether race may ever be considered a factor in government decisions.
Asked for his opinion on that critical issue, Mr. Bush told reporters in the Roosevelt Room on Tuesday, "There are clearly unconstitutional means to achieve diversity. There are race-neutral ways to achieve diversity, which I have put in place as the governor of Texas, and that will lead the courts to define the outer limits of the Constitution."
The Michigan case marks the court's first statement on racial preference programs in public university admissions since the 1978 Allan Bakke case, when the court outlawed racial quotas in university admissions, but left room for race to be a "plus factor."
After Mr. Bush intervened in the Michigan case, the two most prominent African-American members of his administration publicly split with the president on the affirmative action issue.
National Security Adviser Condoleezza Rice said that while she agreed the Michigan policy was flawed, she felt it was appropriate to use race as a factor in the college admissions process. Secretary of State Colin Powell went further, saying he supports the methods the University of Michigan uses to bolster its minority enrollments.
Mr. Bush was asked twice Tuesday for his opinion, saying both times it was up to the court to decide. Republican strategists close to the White House have said Mr. Bush's position is a result of trying to please anti-affirmative action conservatives without appearing to be against racial diversity.
Michigan and many other public universities have used the Bakke ruling to design programs that can help minorities who might be rejected if only test scores and grades are considered.