The University of the District of Columbia Board of Trustees last night rejected, then reversed itself and approved a 29 percent increase in annual tuition after some trustees warned that the school would be in financial jeopardy without additional tuition fees.

On a 7-to-5 vote, the trustees agreed to raise tuitions next fall from $462 to $600 for District residents enrolled in undergraduate progams.

Tuitions for nonresident undergraduates would rise from $2,310 to $2,400. Graduate fees for residents would increase from $1,090 to $1,200, and from $2,310 to $2,400 for nonresidents.

On the first vote that resulted in a 7-to-5 decison against the increase, several trustees said that students had not been consulted and that lower-income students might have difficulty continuing their educations if tuition goes up.

"Raising tuition is not the only way to raise revenues," said Trustee Joseph Webb.

But supporters of the increase arrgued that the university desperately needs higher tuitions to help offset an estimated $5 million budget shortfall projected for fiscal 1987. The tuition increase is expected to offset about $1.3 million of that, university officials said.

"This is critical to the future of this university as a university," said Trustee Lorraine Whitlock. "It will mean great financial jeopardy," she said, if the tuition increase is not approved.

Supporters also said that the board was under pressure from city agencies to begin to bear more of the financial burden at the eight-year-old public university. The last tuition increase at UDC was in the fall of 1984.

You are taking a huge risk . . . that the mayor will sock it to us," Trustee Daniel I. Fivel said to those who opposed the tuition increase on the first round. "There will be a terrible reaction downtown."

UDC has one of the lowest tuitions in the country, according to university officials, but nearly the highest educational cost per student among public institutions.

Voting in favor of the tuition increase were Trustees Ronald Brown, Whitlock, Lucy M. Cohen, Peter B. Edelman, Fivel, Donald A. Brown and Thomas A. Hart. Voting against the increase were Trustees F.D.R. Fox, Virginia H. Howard, Concha N. Johnson, Robert E. King and Webb. Donald Brown and Hart switched their votes after the first roll call in which they opposed the tuition increases. Absent from the meeting were Elizabeth A. Abramowitz and Herbert O. Reid Sr.

Board Chairman N. Joyce Payne last night named nine persons to a search committee to find a permanent president for UDC. Those named included six trustees: Edelman, who will serve as chairman; Hart, Whitlock, Fox, Reid and King. Former UDC president Lisle Carter and faculty Senate President Wilmer Johnson also were appointed. One more faculty member will be named to the committee, Payne said.

The board also voted to spend $20,000 to pay for consulting fees to help with the search for the successor to Robert L. Green, who resigned under pressure in August.