Lisle C. Carter Jr., president of the University of the District of Columbia, has been named a part-time senior adviser to the new U.S. Department of Education, scotching reports that he would leave the university to become the department's undersecretary.

"There have been rumors of all sorts," Carter remarked at a meeting of the university trustees last night.

"But I should say to you this evening: I ain't going nowhere. I plan to continue as president of the university."

Earlir in the meeting, Carter announced that UDC had won accreditation from the Middle States Association of College and Schools.

In a letter dated Dec. 10, the association said it was "impressed by the progress" that UDC has made in consolidating the city's three former public colleges. But it said the university was "seriously handicapped" by the scattered pattern of its buildings, and urged that approval be given for a new downtown campus, which the university is seeking to build near Mount Vernon Square.

The Washington Post reported early this month that White House officials had asked Carter to take the number two job in the new federal department, which was approved by Congress last summer but still has only one official employe -- its secretary, Shirley Hufstedler.

Yesterday Carter confirmed in an interview that he had "conversations with people at the White House" about becoming undersecretary of education, but he said the job had not been formally offered to him.

"I said all the time it was not something I was in a position to do," Carter said. I have to pursue my responsibility here at the university."

A spokesman for Hufstedler said Carter would serve as her "senior adviser" during the transition period until the department begins official operations, probably in early June.

The spokesman said Carter would work several days a week advising Hutstedler on policy and also helping her evaluate candidates for high-level jobs. He will be paid by the federal government while working on department business, the spokesman said, although the amount is "subject to negotiation."

In the statement announcing his part-time appointment as adviser to the Education Department, Carter declared that his "professional obligations [to UDC] preclude me from considering a long-term commitment to a high post in the department at this time."

Carter, 54, became president of the university here in October, 1977. He has a five-year contract which expires in 1982.

Before coming to UDC he was chancellor of the Atlanta University Center and had also been an assistant secretary of Health, Education and Welfare during the administration of Lyndon Johnson.

UDC, which has about 15,000 students, was formed in 1976 through a merger of Federal City College, Washington Technical Institute and D.C. Teachers' College. All three institutions had previously been accredited by the Middle States Association, but the merged university was required to win accreditation on its own.

In its letter granting accreditation for five years, the association said that its evaluation team had issued a highly favorable report following a visit in September.

The association said "it was favorably impressed . . . by the progress made toward consolidation in a relatively short time, particularly in the face of internal tensions, external opposition and political meddling." But the group said it was "concerned about the complexity of the [university's] external relationship" because UDC is subject to control by both the D.C. government and Congress.

It said the university's scattered building "make internal communication extremely difficult," and praised UDC's plan to build the Mount Vernon campus in addition to the large campus already under construction on upper Connecticut Avenue at Van Ness Street.

Sen. Patrick Leahy (D-Vt.), chairman of the Senate D.C. Appropriations subcommittee, has said he doubts that the campus is needed.