Shari Barton Kharasch, who presided over last month's confused primary balloting as chairman of the - D.C. Board of Election and Ethics, submitted a delayed-action resignation yesterday that would keep her in office until after the city's new mayor is elected in November.

Kharasch asked Mayor Walter E. Washington to withdraw her nomination for a second three-year term, and said she will step down from the job Dec. 15.

The mayor promptly sent the City Council a terse 28-word letter withdrawing her name from consideration, averting a probable showdown at a committee hearing that had been scheduled for today on the renomination.

Kharasch said she decided on the Dec. 15 resignation date for two reasons - to keep the board membership intact through the general election and the period of legal challenges that might follow, and a desire to attend an international of conference of election officials early in December.

Kharasch said she is on the steering committee of the conference, which will meet in Minneapolis. She said she plans to pay her own way to the event.

A 39-year-old political scientist, Kharasch came under fire from candidates and aides for the board's conduct of the Sept. 12 primary election, which was marred by 12 weary and confusing days of ballot counting that left the Democratic mayoral nomination of Marion Barry in doubt until the end.

Criticism of Kharasch centered on claims of weak leadership of an election organization that, after widely publicized and embarrassing snafus in past years, seemed on its way toward achieving credibility.

Although Kharasch insisted yesterday that she was "not withdrawing because I was under fire," it was clear that her renomination had scant chance of winning council confirmation.

Willie G. Hardy (D-Ward 7), chairman pro tem of the council, who was to have presided over today's hearing on the nomination, said yesterday that "the mayor ought to remove her (Kharasch) as chairman" immediately.

Hardy did not suggest that Kharasch be ousted from member on the three-member board, but urges that the mayor designate one of its other members - Jeanus B. Parks Jr. or James L. Denson - as its chairman.

"Who else do you hold responsible?" Hardy asked as she discussed the Kharasch withdrawal with an interviewer. "There has been no good leadership . . . Don't blame the (vote-counting) machines. It's the leadership."

An aide to Sterling Tucker said the outgoing council chairman, who along with the mayor was defeated by Barry in the primary election, agreed that Kharasch should be removed from the chairmanship.

Barry told reporters that he believed Kharasch should stay on until after the November election, saying her removal now "probably would confuse the thing."

If there are disputes in the general election campaign, Barry said, "it would be danagerous to have a two-member boards," which could reach an impasse.

By law, the board is bipartisan, with no more than two of its members permitted to be members of the same political party. Kharasch and Parks are Democrats. Denson is a Republican.

Speaking of Kharasch, Barry said, "I think she took more weight (of criticism) than she should have." He voiced hope that the mayor would not submit a new nomination before he goes out of office on Jan. 2, leaving the appointment to be filled by the winner of the Nov. 7 election - either himself or Republican Arthur Fletcher.

Sam Eastman, the mayor's press secretary, said last night that Washington" is looking at the situation," and has not decided upon Kharasch's tenure.

Kharasch's term on the board actually expired Aug. 11, but the mayor submitted her renomination too late for a hearing before the council took a summer recess. Under D.C. law, she may continue to serve on the board until the council confirms a successor.

The chairman of the board is chosen from among its members by the mayor, and serves in that post at the mayor's pleasure.

After the primary election, and until the electoral board certified the official returns last Wednesday, Kharasch had refused to respond to the criticism of her role or answer questions on her tenure.

She said yesterday that she decided last Friday to ask that her name be withdrawn, and typed a three-paragraph letter to the mayor. The letter, which gave no reason for her decision, was delivered to the mayor's desk yesterday.

The Sept. 12 election, which led to the resignation, was marked by problems in counting challenged ballots, the belated disclosure that there were thousands of ballots left uncounted by the city's electronic scanning equipment, and a shortage of ballots on election day in one Northeast precinct.

After the mayor withdraw her nomination yesterday, Kharasch defended her role to reporters, and said she will continue to push for improvements and reforms in the city's election processes.

This afternoon, she said plans to testify before a council committee for an electoral board budget that is larger than the amount proposed by the mayor. It would provide more personnel and a long-sought computerized voting register, averting many of the problems that have led to large numbers of challenged ballots in the past.

"And I will continue to push for a full-time chairmanship," she said. "I think we can use this attention now to focus on the [board's] problems . . . They involve a whole series of things, and it's mostly [lack of] resources."

Board membership and the chairmanship are part-time jobs, paid at the rate of $12.50 an hour. The chairman may earn up to $26,000 a year.

Criticism of Kharasch came also yesterday from Denson, the board's Republican member; from the Ward 5 Coalition of Better Government, and from Sallie A. Johnston, a former electoral board member and adversary of Kharasch.

Denson said Kharasch was indecisive as chairman and seemed to have a compulsive desire to be liked - points that she rejected. The Ward 5 group and Johnston both urged the mayor to remove Kharasch immediately.