Former D.C. City Council chairman Sterling Tucker asked yesterday that he not be renominated as new head of the D.C. Board of Elections and Ethics, and Mayor Marion Barry said he is having trouble finding someone to take the job.

Tucker, whose nomination by Barry was abruptly rejected by a City Council committee two weeks ago, declined Barry's offer to send his name to the council again.

"I do not feel I would have their full confidence," Tucker wrote in a letter released yesterday. "There still remains the negative perception of how I might function in the job."

Barry said the committee's action against Tucker, which was taken without public notice, has scared off several other potential candidates for two seats on the three-member board, which conducts elections and oversees the city's ethics laws.

"Several of the people I have talked to have declined my request," Barry said, "even though they feel they could do a good job as chair of the board. "Some of them don't want to take the chance of being humiliated by rejection by the council."

Barry said he hoped to have a new name by the weekend. Elections officials have said the difficulty in naming a new chairman is delaying reforms of the elections office, which has been plagued by snarled voter registration rolls and low employe morale.

The Government Operations Committee rejected Tucker by voice vote. Committee Chairman William R. Spaulding (D-Ward 5) said he objected to the fact that Barry had not discussed Tucker's nomination with him, but other council members and the mayor said committee members feared that Tucker, who tried last year to regain his old job as council chairman, might still have political ambitions.

Clifford Alexander, a former secretary of the Army under President Carter and a candidate for mayor in 1974, was considered for the job but said last week he was not interested and was never formally asked. Attorney Karen Hastie Williams also turned down the job.

Several council sources said yesterday that Barry also is considering George L. P. Weaver, a former labor official, for the post. But late yesterday, Weaver, who is semiretired and serves on the board of the Office of Employee Appeals, indicated he may not want the job.

"Why should I be interested in taking on a headache in my stage of life?" Weaver said.