MAYOR MARION BARRY gave local realtors and mortgage bankers an invitation, as well as a warning, when he said last week that they would be "at loggerheads" with the city government "until there is a dramatic breakthrough in the housing supply." The warning reflected the political arithmetic of a city with many renters and lower-income homeowners who feel threatened by the local housing boom. No matter how shortsighted rent control and freezes on condominium conversions may be, city officials will be under strong pressure to continue such expedients as long as the stock of sound, lower-cost housing keeps dwindling.

Politically as well as economically, the only real way to ease the strains is to enlarge housing opportunities for lower-and moderate-income District residents. Mr. Barry and his energetic housing director, Robert L. Moore, seem determined to use every District and federal dollar that they can find. They have already started renovating 733 of the boarded-up buildings that the city owns. The mayor's housing policy draft, released last week, outlines ambitious plans to help lower-income families, strengthen neighborhoods and improve the city's dismal public housing. All this will be discussed with community leaders at a housing "summit conference" on Saturday.

A productive city housing program would be a breakthrough in itself. Yet that alone won't be enough. As the policy draft emphasizes, government simply cannot subsidize everyone who needs housing help. Private investment and initiatives will also be required, on a much larger scale than in the past.

Essentially, Mr. Barry would like to strike some bargains with the real-estate industry. Condominium conversions could be made easier, for instance, if developers agreed to reserve some units for subsidized families, or let some elderly tenants stay on without raising their rents. A developer planning a high-income project in one part of town might be encouraged to help finance lower-income housing somewhere else. More traditional types of incentives, such as low-cost land and tax breaks, could also be used to promote both housing and light industry.

The city is coming into a time when wildfire inflation in real estate is going to make it more onerous than ever to be poor. But given the appeal of in-town development, there are possibilities for useful arrangements. It is an invitation that the private sector should accept. A course of public-private cooperation might be bumpy at times, but it could relieve the current strains and spread the benefits of growth more widely through the community.