D.C. City Council Chairman Sterling Tucker, who ran second unofficially in last week's mayoral primary race, has been offered the post of assistant secretary for fair housing in the Department of Housing and Urban Development.

Sources said HUD Secretary Patricia Roberts Harris made the offer after inviting Tucker to her office last Wednesday, following the District's Democratic primary in which Tucker ran 1,188 votes behind Councilman Marion Barry.

The outcome has been clouded because election officials have been counting some 1,000 absentee ballots and evaluating challenges to about 4,600 votes. A final tally will be announced today, and most political observers expect Barry to win the nomination to succeed Mayor Walter E. Washington, who finished third last week.

Tucker declined to comment yesterday, saying only that he wants District citizens to be "assured that they had a full and fair opportunity to vote in last week's primary and that they are confident that they received an accurate ballot count."

However, a source close to Tucker said he considered Harris' offer of the $50,000 post "a very fine one." A HUD source said the offer was contingent on the election outcome and that Harris had not yet sent any name to President Carter, who will officially make the appointment.

(In the District the mayor's salary is $52,500, and the council chairman makes $38,444 a year).

The Fair Housing and Equal Opportunity Division, which Tucker would head at HUD, has long been considered a troubled, ineffective unit. Frustrated by its lack of action, Harris has forced a shakeup, and last week Assistant Secretary Chester C McGuire Jr. and his deputy, Herman (Tex) Wilson, resigned.

Both are black, and Harris, herself a black, has been looking for a black who is well-known in fair housing circles. Tucker is black, but housing has not been considered his field of expertise, at least in recent years, according to fair housing experts here.

However, in 1972, when Tucker was chairman of the Human Resources Policy Committee of the Metropolitan Washington Council of Governments, he pushed for a "fair share" plan under which each area jurisdiction agreed to take a percentage of federally subsidized housing.

Before that, Washington, Prince George's County and Alexandria had nearly all of the area's assisted housing units.

"Sterling was invaluable in building the consensus needed to make the plan work," said Ruth R. Crone, human resources director at COG." As a result, Washington was one of the nation's first three areas to have fair share programs."

Tucker also appealed successfully to HUD not to shut off money to the area for assisted housing in 1973 when the Nixon administration imposed a nationwide moratorium on such funds, she said.

Tucker, 54, was executive director of the Washington Urban League from 1956 to 1974, when he became chairman of the District's elected city council. He had been vice chairman of the presidentially appointed city council from 1969 to 1974.

From 1968 to 1971 Tucker also headed the National Urban League's "New Thrust" program dealing with urban development, neighborhood renewal and low-income housing in 102 cities.

Two experts in civil rights said yesterday that Tucker is known more for his work in getting jobs for minorities than for pushing for equal opportunity in housing.

One, who declined to be identified said Tucker, "coming from a political defeat, may be handicapped if the job is seen as a dumping ground for fallen political figures. It looks as if that post, where little enough has been accomplished in the past, is cheaply regarded."