Performing like a championship boxer, D.C. Mayor Marion Barry Jr. punched and jabbed at the city's financial establishment today in an effort to win a larger commitment from business in confronting the city's economic problems.

First, he soothed Washington's bankers and encouraged them to relax by boosting the city and giving praise for what he said were evident changes in their attitude about the District in recent years. "I love Washington, D.C.," he told a meeting of the D.C. Bankers Association. "I believe in being No. 1"

Then, speaking to an audience that included not only the city's leading bankers but also bank board members who happened to represent most of the Washington area's other large corporations, the mayor punched out a series of challenges.

"You have to do better" in employing blacks and women in senior managemnet positions and on boards of directors, he said bluntly. It was not a veiled threat, for he also revealed that the D.C. Human Rights office will begin an investigation soon of minority hiring and promotion practices at Washington financial institutions.

Mayor Barry also told the business leaders they must make more of a contribution to bringing new business to the city while keeping the businesses that already exist. And he revealed that one of the financial community's leaders - Riggs National Bank President Daniel Callahan III - has agreed to become chairman of a new Mayor's Economic Development Committee.

In previous administrations, this committee has been largely moribund and its main contributions have been continuous studies of the city's econmic problems. But as these reports were completed and rewritten, businesses continued to leave the city - auto dealerships, printing firms and headquarters complexes for companies such as Hechinger's, M.S. Ginn and People Drug Stores.

Barry told the bankers and their business associates today that "it is not enough" for them to support general business expansion in the metropolitan region or in the wider Baltimore-Washington "common market." The majority of people attracted to new businesses in the suburbs live there and do not contribute much to helping solve the city's own problem at the heart of the region, Barry declared.

In his address to the D.C. Bankers 61st annual convention here at the Greenbrier Hotel, which amounted to a state-of-the-city economy keynote, the mayor conveyed the champion's image of informal confidence. He spoke extemporaneously, dressed with a dark blue jacket and white shirt open at the neck. Barry said he brought along a camera to get some pictures of bankers in their flaming red jackets or light-colored and plaid resort pants, a sharp contrast to the pinstriped suits found inside bank offices.

The D.C. mayor received a generally friendly reception from a bussiness community that mostly had supported one of his oponents in last year's Demoracratic Party primary - either former mayor Walter Washington or former City Council chairman Sterling Tucker. But Barry quipped that he hadn't yet been introduced to anyone who didn't vote for him and he thanked them all for their support.

Repeatedly, the mayor called on the business community to use influence in support of city administration goals - such as control over its own budget, now resting with Congress; location of a new city university campus north of Mount Vernon Square, closer to more residents and a key to that area's development, but currently opposed by Senate District Committee Chairman Patrick Leahy (D-Vt.); and the ability to levy income taxes on suburban residents who earn their living in D.C.

On the subject of more hiring and promotion for women and blacks, the mayor notes that business doesn't want government interference and suggested a method of avoiding this problem. "Do things the government wants," he admonished the bankers, and they will avoid having to fill out long questionnaires.

With the city's work force predominantly black, he added, banks must strike a balance between their needs and those of the city and blacks by making sure there are more blacks and women in the upper echelons of a traditonally white and male business.

"The banking community traditionally has not been involved with the heart of this region . . . but in recent years there have been changes," said the mayor in urging more cooperative efforts.

Charles Daniel, president of Union First National Bank and also president of the D.C. Bankers Association, joined Barry in emphasizing more cooperation by the financial community and city government to solve current problems. He called the mayor a "fighter" for what he believes, who "does his homework and is informed on the the gut issues he faces on a daily basis . . . concerned for all our citizens."

Barry, in his address, focused on the current state of city problems and efforts since he took office in January to bring about change. Among his main points:

The city bears an unusually large share of the region's social costs, with 18 percent of its 700,000 residents over 65 years old and some 200,000 citizens receiving some form of federal or city aid, as well as more than half of all subsidized housing in the area.

Although most land in D.C. is under federal control, the federal payment to compensate for this drain from the tax base is now down to 18 percent of the overall annual budget of $1.3 billion, compared with a 40 percent level in the early 1940s and an even lower level proposed for next year. As a result, citizens and businesses have to pay higher tax rates.

The Barry administration's first economic development goal is to keep existing business. The mayor noted an exodus to the suburbs of auto dealers, retailers and restaurants in recent years and said one solution would be for the city to issue development bonds that help industries build modern facilities. But it may be 18 months before Washington can begin offering such bonds, after a full audit for the next fiscal year.

Because the city is a "professional services town," with few jobs for unskilled and blue-collar workers, a second goal will be to attract new business to redevelopment areas - light industry or computer and electronics firms, including those based in Japan and Germany that need an American manufacturing base.

Another goal is to "convince the federal government" to expand its facilities in the metropolitan area within the city itself. He voiced optimism that D.C. will win a current fight over location of a new headquarters for the Nuclear Regulatory Commission and told the business leaders: "You ought to help us do that."

Plans for a downtown convention center near Mount Vernon Square are "on track." Condemnation proceedings are under way with some property owners challenging the city in court. Land clearing for some of the centre site should start in the fall, however.

The mayor called again for a reciprocal income tax arrangement, noting that no other American jurisdiction has most of its work force living outside and not taxed; most of the states already have income tax arrangements with their neighbors. And he vowed to make it easier for business to deal with city agencies.

Barry warned that with about half of the city's black youths out of work, development of jobs has reached a critical point. He said that a "serious housing crisis" would be solved only with more federal and city subsidies, but this problem would be aggravated by continued conversions of rental units to condominiums at the rate of recent months.

With support from banks and other financial institutions, the city has begun to renovate boarded-up houses, and by fall, the mayor said, D.C. will be ready to enter the bond market through a new housing finance agency that will raise money for needed construction.

Kinney declined to discuss the tourism effort because it still is in the formative stages, she said. But one person who attended last week's meeting said Barry hopes to announce a major campaign to promote D.C. travel by next fall.