Mayor Marion Barry, responding to viewers' questions on a televised call-in program last night, described the District governmant as one with limited resources and a limited ability to solve the city's problems.

Barry said the city's shortage of low-cost housing, the needs of elderly persons living on fixed incomes and even the city's own worsening budget crisis were issues over which his administration does not have full control.

The mayor's remarks came at the Northwest Washington studios of WJLA (TV-7) before a studio audience of 35 persons. Another 175 persons watched the broadcast from Logan School at Third and G streets NE, and 180 others tried to phone in questions.

After several questions about housing and the administration's efforts to stem the flight of middle-class blacks to the suburbs, Barry said the problem was beyond the District government's reach.

"These problems will not be solved by this government itself," he said. "I'm not ever going to say this administration can build enough housing to take care of our needs."

Barry said the city would need "tremendous assistance from the federal government" to rehabilitate and subsidize housing.

An elderly woman reminded Barry that "we need food to live in these houses" and asked what the government was doing to help senior citizens living on fixed incomes.

After listing programs which included meals for the elderly and more convenience in obtaining food stamps, Barry told the woman, "We don't have enough resources in my view to take care of all your needs."

Discussing the budget crisis, Barry again called for outside assistance, blaming the Congress for not approving a sufficiently high federal payment for the District. He said the federal government has "some responsibility" for the city's fiscal problems, and also laid some blame on the administration of former Mary Walter Washington.

Barry declined to comment when asked yesterday about the decision of House-Senate conferees to give the city a supplemental federal payment of $38.3 million -- substantially less than the $61.8 requested by Barry.

The mayor, maintaining his public hands-off position, declined to tell one caller whether he favors a city lottery as a revenue producing measure.

Barry also defended the city's beleagured summer jobs program for youths, saying a decrease in the number of available jobs -- about 2,000 fewer than last year -- on poor response from the business community.

Barry defended his 6 percent tax on gasoline, a revenue-raising measure passed by the City Council this week, as a fuel conservation measure. "It doesn't make any sense that on the one hand you're spending $54 million (in Metro subsidies) for public transportation and on the other hand you're not doing anything to discourage the use of the car," he said.