A D.C. City Council committee handed Mayor Marion Barry a stunning defeat yesterday by rejecting the nomination of former council chairman Sterling Tucker to head the city's troubled Board of Elections and Ethics.

The voice vote, which also killed the nomination of Valerie K. Burden to fill a second seat on the three-member board, came after Barry spurned private appeals from some council members that he withdraw the nominations to avoid embarrassing Tucker, who served as the council's first elected chairman from 1975 to 1978.

The vote by the committee on government operations marked the first time a council panel has rejected any mayoral nomination, according to council staff members. Barry and his aides were visibly shocked by the defeat and news of the committee's action spread quickly throughout council offices at the District Building.

Barry, first told of the vote as he was entering a waiting car at the District Building, brushed aside a reporter's inquiries and said brusquely, "I don't know what they've done." He then slammed the door of the car and it drove off.

"They just simply did not want Tucker in the job," said one council member after the vote. Many members of the council said Burden "was just caught in the wake" of an action directed at Tucker.

The rejection of Tucker and Burden is expected to delay further already lagging efforts to clear up the city's confused voter-registration rolls and the administrative chaos that has snarled several recent elections.

Several committee members have complained privately that Tucker, who lost a close race for mayor in 1978 and a bid last year to regain his old job as council chairman, has been too involved in politics to run the board impartially.

Barry reacted quickly and sharply to the committee action. In a written statement, he criticized the committee for taking the vote without public notice and after it had scheduled a public hearing on the nominations for March 28.

"Certainly a public hearing would have been more appropriate. By this action, which was not part of the committee's agenda, the citizens have been done a disservice," Barry said. The mayor also criticized the committee members for failing to suggest nominees to him.

Tucker could not be reached for comment.

Council member William R. Spaulding (D-Ward 5), chairman of the committee, said the vote was a protest against what he said was Barry's refusal to discuss the nominations with him before making a commitment to send them to the council.

However, some council members and a high-ranking aide to the mayor said there had been numerous discussions about Tucker's nomination since early February before it was submitted to the council.

Three members of the five-member committee--John Ray (D-At Large), Jerry A. Moore (R-At Large) and Charlene Drew Jarvis (D-Ward 4)--face reelection bids next year.

Jarvis, Ray, Spaulding and other members of the council--including John A. Wilson (D-Ward 2), who is not a member of the committee--have privately opposed Tucker. Wilson's term also expires next year.

"There have been too many disasters in that job; we want a professional," one council member said. "The mayor can punish his enemies by using the Board of Elections and Ethics."

In addition, one council member said that Barry "backed us against the wall" by suggesting the council would not publicly reject Tucker because of his past association with the council. Barry "thinks he can do anything he wants to do," the member said. "He has killed us the council too many times in the past. At some point, the council has got to come to the conclusion that we have to say, 'no.' "

There was no indication last night whether Barry would seek to resubmit the names of either Tucker or Burden as nominees or offer other candidates.