The Washington-area office of the U.S. Department of Housing and Urban Development has granted only conditional approval of the District of Columbia's $24.1 million community development fund for the new fiscal year, citing continued shortcomings in the city's housing and development programs.

The action ties strings to the city's right to spend the money and will prevent aided housing activities at least during the next three months, Robert L. Moore, the D.C. housing director, said yesterday.

The conditional approval for the city's programs was given Sept. 26 by Terry C. Chisholm, area manager for HUD, in a letter to Mayor Marion Barry. While not citing any illegal actions by city officials, Chisholm said there were many deficiencies in the city programs and asserted that the city "does not fully comply with all applicable requirements, laws and regulations" and has failed to submit adequate reports.

Chisholm said the city has an inadequate financial management system, that it has failed to monitor standards required by federal law for wage rates of workers and that it has shown bad judgment in deciding who should get loans for housing rehabilitation.

Moore, in an interview, denied many of Chisholm's findings, and reacted angrily. He said he would appeal to HUD's national headquarters to have them overturned so the city could continue its program without restraints. He contended that, despite great improvement, the District is being punished for a mess the Barry administration inherited in January 1979 from former mayor Walter E. Washington.

"I think in the past year and a half, we have done a superlative job," Moore said. "We have 5,000 housing units under way. I will stack our record up against any city in the country -- compare us with New York, Chicago, anywhere else."

The money involved in the HUD action is called a community block grant. Some years ago the federal government stopped making individual earmarked grants for such programs as low-rent public housing, urban renewal, neighborhood rehabilitation and relocation of displaced families and began making lump-sum payments to cities that qualified for aid. In the District, the annual block grant pays the bulk of the cost of operating all housing programs.

Because Chisholm's decision rations the speed at which the District can spend the $24.1 million conditional grant, Moore said the city can maintain existing projects but not embark on new ones.

Moore said overhead costs in his agency consumed 47 percent of all the federal grants under the previous administration, a figure that has been slashed to under 19 percent now.