D. C. City Council Chairman Sterling Tucker promised yesterday that if he is elected mayor there would be a wide reorganization of the city government, much tighter management of city programs and a host of new faces to operate D.C. agencies.

"A priority order of business must be getting the house of government in shape so that it can function," Tucker declared. "It means organizing it in such a way that services can be delivered . . . and making sure that there is an organization and management and systems of government that work."

Tucker said that as mayor he would ask for the resignations of all city agency heads and then only retain certain officials that he feels are doing a good job. He cited the names of nine department chiefs he would either fire or place in different jobs.

Throughout a 75-minute luncheon interview with Washington Post editors and reporters, Tucker portrayed himsef as the Democratic mayoral candidate with the years of proved leadership necessary to head the city government in the next four years.

"Look at the record," Tucker said, citinga litany of his accomplishments an executive director of the Washington, Urban League and later as an appointed and elected City Council leader. "I can lead; I've been successful."

"Each job I've had, each function, each responsibility I've had, I've left it in better shape than it was before I got there and it's been strengthened by it," Tucker asserted.

During the interview, Tucker conspicuously avoided mentioning the names of his chief rivals in the Sept. 12 party primary, Mayor Walter E. Washington and council member Marion Barry. Tucker left it clear that he thinks the city and its government would be better run if he takes over as mayor next January. Asked what D.C. residents could expect by 1982 if he is mayor, he replied:

"You would have a job. Your children would be getting quality education. You'd be living in a house you could afford. Your neighborhood would be stabilized. There would be a city with broader opportunities of various kinds and you would have a greater sense of security of person and home and community."

Time and again, as he discussed a broad range of city problems, Tucker pledged to strickly enforce a D.C. government requirement that 25 percent of all city contracts be given to minority firms - something he said the mayor had not done. Tucker then added, "A mayor has to take the lead. A mayor has to let his people know what he wants and what he expects and they have to know he's serious.

"And . . . if they don't do it, the mayor has to find a way to put somebody else in those positions," Tucker said.

In the same vein, Tucker said he once urged Mayor Washington to fire Joseph P. Yeldell, the mayor's one-time close adviser now indicted on bribery and conspiracy charges.

"And he said under civil service procedures it's not possible," Tucker said of the mayor. "I said do it and see what happens. And I think . . . you've got to take the lead and got to exercise initiative."

Tucker, dressed in a three-piece chocolate brown suit, frequently gestured with his arms as he stressed the changes that he would make as mayor. He said that in the expectation of winning the election he already is creating a committee of business, civic religious, government and community leaders to search for the best possible talent to join the D.C. government.

Tucker said he is certain that some current D.C. agency and department heads "would not qualify for my administration."

One of his chief appointments, he said, would be to name a person schooled in urban affairs and government management as city administrator to oversee "the nuts and bolts" of city programs. He said that was particularly important so that he, as mayor, would be free to "shape the government" and set goals for the city.

While saying that he does "not like the notion of a hit list," Tucker nonetheless named several city officials who would not be part of a Tucker administration. Among those to go, he said, would be city planning chief Ben W. Gilbert, housing director Lorenzo Jacobs, human resources director Albert P. Russo, consumer affairs head Bettie J. Robinson, general service director Sam D. Starobin, human rights director James W. Baldwin, labor department head Thomas A. Wilkins and acting corporation counsel Louis P. Robbins.

Tucker said he would retain police chief Burtell M. Jefferson and chief Jefferson W. Lewis of the fire department.

Tucker conceded that existing city civil service rules may prohibit him from immediately getting rid of all city officials he wants dismissed. "It may cost the government a little money" to retain the officials for awhile, he said.

Tucker quickly added, "There's one thing certain: those who are not qualified for the jobs will not be in those jobs in a Tucker administration."

Tucker said that improving the city's housing stock, creating more jobs and upgrading the city's school system were the three most critical problems facing a new mayor.

"There are major housing problems," Tucker said, charging that the city has missed numerous opportunities to use federal funds to rehabilitate homes and to help poor people buy homes.

He said the lack of "stability of neigborhoods . . . makes people jittery about their ability to able to afford to live in the city. It's fundamental cornerstone of the community and the neighborhood."

Tucker said the District of Columbia government has to creatively package federal and private money to subsidize lower-income residents' purchases of homes so that they will not be forced to move.

"It's a matter of understanding what tools are available," Tucker said. "It's a matter of packaging. It's especially a matter of leadership."

He said that because of the failure of the city housing programs and a lack of comprehensive planning "the city's just been kind of growing on its own, without any shape, without any direction, without any leadership.

"My view of the city is that we have responsibility for making it possible for the least of us to have a place to live, in housing that they can afford, which is decent, safe and sanitary," he said.

On other matters, Tucker said he:

Does not think "it's necessary right now to raise any additional taxes." He said the District of Columbia must push for enactment of a tax on the incomes of the 280,000 commuters who work in the city each day and secure a federal payment to the city that does not fluctuate each year.

Opposes creation of city-run lottery, describing it as a means for "taxing the poor."

Would create a city office to find every federal grant for which the District of Columbia is eligible. He said the current government "does not know what's available to it."

Plans to reorganize the city's largest agency, the Department of Human Resources, both in terms of its structure and "assignment of responsibility." He said the first step in the reorganization would be to assess the social welfare needs in the city before deciding how best to break up the agency.

"It has to be restructured," Tucker said, "It has to have the leadership which can see the broad range of responsibilities."