The FBI began a preliminary investigation yesterday of alleged financial improprieties at the University of the District of Columbia, according to an FBI spokesman.

The launching of a federal criminal investigation came one day after U.S. Attorney Joseph E. diGenova said his office was reviewing a letter received Monday from UDC Trustee Joseph Webb that raised questions about expenditures of public funds by UDC President Robert L. Green and other high-ranking UDC officials.

"Certain allegations have been presented to the FBI through the U.S. attorney's office and a preliminary investigation is being conducted," said FBI spokesman Dave Divan.

FBI sources said the investigation will focus on a broad array of allegations involving UDC officials.

Green, 51, defended his record as a university leader and a civil rights activist in an address to the Capital Press Club last night, but declined to respond to questions about alleged misconduct within his administration or the FBI investigation.

"My lawyer has instructed me to make no substantive comments at this time on any of the matters that have been recently reported on because he is examining whether or not there have been deliberate attempts, which he believes there have been, to silence the kind of leadership related to bringing change to UDC," Green said.

"Furthermore, it is my attorney's belief that I may well have grounds for major lawsuits based on deliberate defamation of character, whether by libel or slander, and based upon deliberate and unprofessional conduct on the part of selected individuals," he said.

Gilbert A. Maddox, a UDC spokesman, said yesterday that the Green administration had not received a copy of Webb's letter to the U.S. attorney and that UDC officials were unaware of any FBI probe.

"If the FBI has something it wishes to discover, it certainly has the right and obligation to carry out its responsibilities," Maddox said.

This latest development in the three-month-old controversy at UDC coincided with a statement of support for Green by student Trustee Robert E. King, who accused the news media of trying to destabilize the university and criticized some board members for moving to oust Green.

At least five of UDC's 15 trustees interviewed during the last week said that they favor Green's resignation, although most declined to be identified publicly. A Green supporter, who also declined to be named, acknowledged yesterday that the president is losing ground with the trustees. Webb is the only trustee to publicly call for Green's ouster.

Five board members are solidly behind Green, two are moving away from supporting him and the views of the remaining three are unclear, according to trustees contacted during the last few days.

Several trustees told The Washington Post that board member N. Joyce Payne, executive director of a national higher education association, had contacted other trustees seeking support for an effort to get Green to resign. According to these trustees, who said they support the motion, Payne was attempting to work out a plan that would enable Green to leave UDC "with honor."

D.C. Auditor Otis H. Troupe has questioned Green's use of thousands of dollars of UDC funds for travel, consulting and personal items. After the trustees ordered an independent audit of expenditures by the accounting firm of Coopers & Lybrand, Green recently conceded some of his expenditures were improper and reimbursed the university for $2,332.

Webb's letter to diGenova contained about 20 areas of concern and raised questions about the transfer of UDC's endowment from one bank to another, the employment of UDC board Chairman Ronald H. Brown's wife in the D.C. government, the use of UDC funds for political contributions and for furnishings at the university residence and alleged "cronyism."

A student leader who appeared with King at an afternoon news conference at UDC criticized Webb for requesting a federal investigation.

"We believe the problems of UDC should be handled inside the university rather than outside it," said Gary Thompson, president of the university Student Government Association. " . . . We believe that Joseph Webb has violated the fiduciary responsibility of the board as regards information dissemination."

Webb, one of three alumni trustees, said yesterday, "I don't believe Mr. Thompson knows what my fiduciary responsibilities are. My fiduciary responsibility is to advance this university."

Webb said he believed a federal investigation would have more credibility than an internal probe in the eyes of congressmen who will be considering the budget of the publicly financed university this fall.

"What I have done is simply ask that the university be exonerated," Webb said. "I didn't say to the federal prosecutor, 'Come in and find Robert Green guilty of anything.' I said, 'Launch an investigation of the board and university.' "

King told a small gathering of students and reporters that "constant turmoil and frequent changes" at the high levels of the university were an impediment to its development.

"Since the beginning of this vicious and venomous attack by The Washington Post and The Washington Times on the integrity and credibility of Dr. Green and the university, the suspicion among the black community has been that the press has a hidden agenda," King said. He said the agenda included the "destabilization of our university's operation" and the "denigration of its reputation."

King and Thompson also distributed "fact sheets," prepared by Green's staff, that cover the charges against Green and his responses to them as well as outlining his accomplishments as president. Thompson said 15,000 "fact sheets" would be distributed to students, who will begin registering next week for the fall semester.

Thompson said Green had received a vote of confidence from the Student Government Association's executive council, interim student council and university council -- organizations comprising elected student leaders and leaders of campus organizations and clubs. Thompson said the vote was conducted by telephone and that 75 percent of the respondents supported Green.

At the speech last night, Green appeared with his wife, Lettie, and two of their sons, Kurt and Kevin. Green listed his accomplishments since taking over as president of UDC in September 1983 and said the university community supported his efforts.

In an apparent reference to the controversy over the university's finances, Green said he had come under "a great deal of pressure from within and outside the institution." But the UDC president said he had been under pressure before and reminisced about his experiences in the civil rights movement.

He said he provided leadership in the effort to desegregate housing in East Lansing, Mich., home of Michigan State University where he once served as a dean. "I provided the leadership to end the discrimination against black students at Michigan State," he said. "I came under a lot of criticism for that . . . . Pressure is not something I'm unfamiliar with."