The Justice Department yesterday asked the Supreme Court to decide how far states that once operated separate white and black colleges must go to desegregate their higher education systems.

The department said it believed a lower court erred in ruling that Mississippi colleges need do no more than open themselves to students of any race. The department is arguing that the state's colleges have perpetuated racially divided schools by granting admission solely on the basis of test scores and by duplicating programs offered by black colleges at predominately white institutions.

The department's action is the latest step in a 15-year-old challenge to Mississippi's higher education system. The state had operated five whites-only colleges and three black colleges until at least 1962, when James Meredith was admitted to the University of Mississippi under court order.

The state has since opened both the black and white colleges to all students, and argues that such "race-neutral" policies have satisfied its obligation to end its discriminatory system. In an opinion in September, the 5th Circuit Court of Appeals in New Orleans agreed.

In asking for a hearing, the Justice Department said the 6th Circuit had taken a different position in a case dealing with Tennessee colleges. The 6th Circuit first required that a white college and black college merge, then upheld a set-aside program giving black students preference for admission to graduate and professional schools.

"An affirmative duty applies to public higher education as well as to education at the elementary and secondary school levels," the 6th Circuit judges said in 1979.

Janell Byrd, an attorney with the NAACP's Legal Defense and Education Fund, welcomed the Justice Department's action, saying, "With this administration it's been particularly difficult to tell what's happening on civil rights."

The department took a position at odds with civil rights advocates in a Supreme Court desegregation case involving Oklahoma City public schools that was decided earlier this month. Department attorneys sided with the Oklahoma City school system in the case, in which the court made it easier for school districts to get out from under court-ordered busing plans.