District Mayor Marion Barry, reversing his longstanding opposition to a plan to create a new public law school, has agreed to cooperate with D.C. Council members in searching for a site for the school and placing it under the aegis of the University of the District of Columbia.

Barry yesterday described his turnaround on the law school issue as a "meeting of the minds" between the administration and the council that was formalized in a agreement signed Friday night.

Dwight S. Cropp, the mayor's director of intergovernmental relations, said yesterday that the mayor was not pressured into changing his mind but felt that "this thing has been dragged out for over a year and too much energy and too many resources have been wasted" on the dispute.

On June 19, Barry vetoed a council-passed measure that would have designated the UDC-owned Wilson Teachers' College building on Harvard Street NW as the site of the proposed law school. Cropp said yesterday that the mayor's veto would have been upheld, because law school supporters on the council were unable to glean the nine votes needed for an override.

Clarke, who negotiated the agreement with Cropp on behalf of council member Hilda H.M. Mason (Statehood-At Large), who chairs the council's education committee, expressed satisfaction yesterday with the new plan.

"It's what the council wanted all along," said Clarke.

Under the negotiated agreement, which has not yet been presented to UDC trustees or to the law school's five-member interim board, the council will drop any attempts to override Barry's veto and the mayor will, according to Cropp, "fully provide leadership in identifying and securing an appropriate, permanent facility for the public law school."

The legislation creating the law school would be amended to:Drop the requirement that staff and faculty currently employed by the Antioch School of Law on 16th Street NW be hired by the new public law school. Make the law school part of UDC immediately and make the law school board subordinate to the UDC board of trustees. Hold UDC's budget harmless from any losses the law school might incur. Provide that Antioch University of Yellowsprings, Ohio, the current school's parent institution, retain responsibility for students graduating through June 1988. The city, however, will offer the school financial support to complete any public-interest cases that have already been undertaken on behalf of D.C. residents.

"The mayor believes that the UDC board of brustees can buy this agreement, and he is going to urge them to accept it," said Cropp.

N. Joyce Payne, chairwoman of UDC's board of trustees, said yesterday that she had not yet been informed of an agreement. But she added that UDC trustees have been working on similar proposed amendments to the law.

"We hope to make the best out of a situation that we feel was not in the best interest of either institution," Payne said. UDC trustees are scheduled to meet with the law school's interim board of directors Tuesday.

Barry's change of heart on the law school proposal represents the first good news law school supporters have had since the council passed the legislation creating the institution in February. Barry, who has said that the school would cost too much and burden UDC, had refused to cooperate in planning or site selection for the institution.

Two members of the institution's interim board, who had not been briefed on details of the plan yesterday, said that they will be extremely pleased if the mayor's reversal stands. "This whole thing has been silly," said board member Frederick B. Abramson.