The Reagan administration yesterday refused to support the Norfolk School Board's attempt to win federal court approval of a controversial plan to abandon mandatory busing of elementary school students to achieve racial balance.

In a motion filed in U.S. District Court in Norfolk, H. Bradford Reynolds, head of the Justice Department's civil rights division, maintained the board lacked legal grounds to ask for the court's blessing before implementing its plan.

"School boards simply cannot invoke the aid of federal courts to render advisory opinions," Reynolds contended.

Both school board attorneys and black community leaders went to Washington seeking Justice's support after the board voted in February to abandon crosstown busing that had successfully integrated public schools.

The school board wanted Justice to back its neighborhood schools plan while the black representatives asked that the department either oppose the plan or not get involved. Norfolk City Attorney Philip R. Trapani said last night Justice's position "was not unexpected." A lawyer for the opponents declined comment.

The controversial plan, supported by the board's four-member white majority and by one black in its vote two months ago, would make Norfolk the first city in the nation to successfully desegregate by busing and then abandon those integration efforts, according to some attorneys.

The proposal is designed to slow the flight of the white middle class to Norfolk's suburbs, mainly nearby Virginia Beach, according to the plan's backers. Opponents have branded it unconstitutional and discriminatory.

In order to gain court approval of the proposal, Norfolk lawyers have asked a federal judge to reopen a 1956 desegregation case that led to court-ordered busing in the city in 1971. It is that action that Reynolds said Justice opposes, largely on procedural grounds.

District Judge John MacKenzie dismissed the lawsuit in 1975 after declaring the school system unitary, or free of discrimination.

"The 1975 dismissal of this case returned the operational control of the school system to the Norfolk School Board as completely as the control exercised by any other school district not subject to a desegregation court order," Reynolds said. "The board is plainly not required to seek prior judicial approval before its plan can be implemented."

The board has said its neighborhood schools plan would leave 10 of the city's 35 elementary schools more than 95 percent black. It has also has filed a suit against four black parents and their children, contending that the defendants oppose the plan's implementation. The suit could serve as an alternate vehicle for court review of the plan if the 1956 case is not reopened.