Lisle C. Carter Jr., the first president of the University of the District of Columbia, said last night that he would step down from his post after his five-year contract expires in 1982.

Carter, 55, said that the foundation for the publicly supported university has been laid, and that he is not prepared to commit himself to providing the long-term leadership that he said will be needed for UDC to realize its potential.

The disclosure of Carter's plans to leave the university post comes a day after Vincent E. Reed announced his resignation as superintendent of the city's public school system, which involves primary and secondary schools.

When he came here in 1977 from his post as chancellor of the Atlanta University Center, Carter said, his objective was to merge into a single university UDC's three predecessors -- Washington Technical Institute, Federal City College and D.C. Teachers College.

With that largely done, Carter said in a letter to the head of the university's trustees, UDC now needs "sustained leadership" through the 1980s to make of it the "outstanding public university" he said it promises to be.

Although he said in an interview he had no specific future plans at this time, Carter said he is not prepared to make the commitment the university's presidency will require, and hence wants to give the trustees ample time to find a successor.

He specifically denied that the change of presidential administrations or other political considerations influenced his decision.

Marjorie H. Parker, head of the trustees, expressed "the deepest personal and professional regret" at Carter's decision. She also announced formation of a committee to find a successor.