City Council Chairman Sterling Tucker conceded last night that he lost the Democratic nomination for mayor City Council member Marion Barry in the Sept. 12 primary.

"I congratulate Mr. Barry on his victory in the Democratic mayoral primary election," Tucker said in a statement issued by his office.

"I urge the Democratic Party to unite in preparation for the general election campaign and I offer whatever assistance may be helpful in that regard," Tucker said.

In the confusion that followed efforts by the D.C. Board of Elections and Ethics to tabulate the results of the vote. Tucker remained silent on the election for days.

Last Friday, he called a news conference to denounce the city's vote counting procedures as a "farce." Tucker said then that he intended to askd the D.C. Superior Court to stop the board from certifying the results and order a new election, based on alleged irregulaties in the balloting and counting process.

The board is expected to certify the results this afternoon.

Tucker's lawyer, R. Kenneth Mundy, said yesterday that 20 affidavits were collected in Tucker's behalf, from voters and precinct workers throughout the city. Mundy said in a statement that he advised Tucker that the sworn statements contained "confirmed instances" of "serious irregularties" during the balloting.

At a hearing at Superior Court Monday, in a case involving Ward 5, Judge George H. Revercomb ruled that under D.C. law, challenges to election procedures must be brought directly to the D.C. Court of Appeals, which has administrative review power over the elections board.

In light of Revercomb's ruling, and based on his evaluation of information contained in the affidavits, Mundy said he had advised Tucker to pursue his allegations through the board's general counsel, Winfred R. Mundle.

Mundy said he gave Mundle "complete information and documentation of the charges" at a meeting yesterday. As a result, Mundy said, Mundle has agreed to investigate the contents of the affidavits. Mundle agreed to recommend the the elec- tions board penaliez anyone found responsible for the alleged irregularities and forward to the U.S. attorney's office any action that may have constituted criminal conduct. Mundy said in his statement.

Tucker said he fully supports the agreement "as a proper alternative to the legal remedy I had planned to seek . . ."

The elections was a hard-fought contest between Tucker. Barry and Mayor Walter E. Washington. Unofficial final results announced on Sunday showed Barry with 32746 votes. Tucker with 31232 and Washington with 29837. Washington has yet to say aanything publicly about the election.

In a related development, Sen. Charles McC. Mathias (R-Md.) has asked for a Senate inquiry into the "unaccountable" delays and mix-ups that beset the primary election.

In a letter dated Monday to Sen. Thomas F. Eagleton (D-Mo.), chairman of the subcommittee on governmental efficiency and the District of Columbia. Mathias said it is incumbent on the subcommittee "to at least take a close look at the District of Columbia Board of Elections and Ethnics to determined how it functioned during this most recent election."

Mathias said yesterday Eagleton's subcommittee, of which Mathias is the ranking minority member, should hold hearings to determine whether it is necessary for the city "to obtain the kind of voting machine technology or other help" to assure election results that are "reliable and accurate and prompt."

Also contributing to this story was Washington Post staff writer Paul W. Valentine.