N. Joyce Payne, the newly elected chairman of the board of trustees at the University of the District of Columbia, said yesterday she is committed to improving the board's sometimes uneasy relationship with Mayor Marion Barry and D.C. City Council members, who have criticized the trustees for failing to monitor the expenditures of former president Robert L. Green.

Payne, 44, who was elected unanimously Tuesday night after Barry's legal counsel, Herbert O. Reid Sr., withdrew from the race for board chairman, appeared eager to repair rifts between the District building and some trustees that emerged during the Green controversy.

"I want to emphasize the critical nature of our establishing a close relationship," she said during an interview yesterday. "We are a city agency and we can't overlook that fact. I will work as closely with the mayor as I possibly can."

Payne, who is director of an association specializing in higher education, said she was in the process of arranging a meeting with Barry.

Barry had made clear in recent weeks that he preferred Reid for board chairman. But Reid surprised some of his colleagues on the board by announcing at Tuesday's meeting that he had decided to withdraw from the race. A number of trustees had said they could not support Reid for chairman because of his close relationship with the mayor.

Payne takes over during an unsettled period at UDC, when the FBI and a federal grand jury are investigating alleged financial improprieties by the Green administration. Green resigned under pressure on Aug. 23 after disclosures in the news media and by D.C. Auditor Otis H. Troupe that he had spent thousands of dollars of UDC funds on travel, consulting and personal items.

UDC officials and trustees interviewed yesterday said they hoped that Payne, who is viewed as politically independent, would be able to unite conflicting factions on the board and within the university community that surfaced during the crisis over Green.

"She is a bright woman and she has some very definite ideas of where she wants things to go," said one senior UDC official. "Her Achilles' heel might be the political end. Her challenge will be to master the politics of the board and to find consensus issues to bring the board together."

The most critical issues facing the trustees in the next few weeks are the search for an acting president to replace interim president Claude A. Ford and the thorny issue of whether to cut a number of senior administrative positions filled by Green.

The board has not yet decided whether to retain provost Maxie C. Jackson, who was appointed by Green and whose contract was to expire the same time as Green's, in September 1988.

Jackson also is entitled to a faculty position in the college of education, according to university officials.

The Green administration hired more than 20 new staffers in the executive branch, a sore point with a number of City Council members who have complained that UDC has one of the most top-heavy administrations of any public university in the nation.

During a private session Tuesday night, the trustees' personnel committee instructed Ford to identify in the next 30 days administrative positions that could be cut, several trustees said yesterday.

Payne said yesterday that the personnel committee will make recommendations about staff positions but that she does not foresee any "radical" changes.

She said there may be "a gradual realignment" within the administration.

Payne also said the university needs "to overcome media exposure" that has resulted from "two months of turmoil" over Green's expenditures of university funds.