Lawyer Patricia Roberts Harris, a candidate for the Democratic nomination for mayor, yesterday used a rundown Southeast Washington public housing project as a backdrop to sharply criticize Mayor Marion Barry's handling of federal housing subsidies.

Harris contended that the Barry administration was five months late in applying for about $20 million in 1982 federal operating subsidies for public housing--a claim disputed by city officials.

She also said the delay may cost the city $500,000 in interest that it could have earned if it had obtained a portion of that subsidy by now and invested it before use. The subsidy is used to make up the difference between the low rents paid by tenants and the actual cost of operating and maintaining public housing.

"I charge gross negligence and gross incompetence in meeting the needs of public housing residents," Harris told a gathering of reporters and residents at a courtyard in the Fort Dupont housing project, near Ridge Road and C Street SE.

However, Harris, a former head of the federal Department of Housing and Urban Development (HUD), declined to offer proposals of her own for improving housing conditions for low-income families, although her appearance had been billed by aides as a major statement on housing.

Harris has been criticized by some of her opponents for missing about half the mayoral candidates' forums and for refusing to take firm stands on a wide range of issues since she formally entered the race three months ago.

"She ought to put forward what she would do," said Ivanhoe Donaldson, Barry's campaign manager. "The mayor has done an aggressive job on housing all across the city. I think that just criticizing is easy."

D.C. City Council member John Ray, another Democratic candidate for mayor, said Harris has conducted a negative campaign, attacking Barry's performance and record without indicating what she would do differently.

"Anyone can call a press conference and show off dilapidated housing in the city," said Ray, who has issued three major campaign position papers since March 18. "But just criticizing past performance doesn't solve the problem."

Said Council member Charlene Drew Jarvis (D-Ward 4), who also is seeking the nomination: "It certainly is characteristic of Mrs. Harris as a candidate not to have specific proposals and solutions."

Harris said yesterday that she would not be rushed into releasing a long-promised series of campaign position papers. She said there would be plenty of time for that before the Sept. 14 primary.

"I make my own schedule," she said.

Harris arrived at the press conference clutching the hands of two little children who live in the neighborhood. Mary Williams, president of the Fort Dupont Resident Council, endorsed Harris for mayor during the press conference.

"We are not one-issue voters, but housing is our most pressing problem and she [Harris] has administrative experience--she knows HUD," Williams said.

Harris complained that the city's Property Management Administration (PMA) has done a woefully inadequate job of responding to residents' complaints about broken door locks, leaky roofs and ceilings, flooding and trash and broken glass strewn on the grounds.

Sidney Glee, the head of PMA, said yesterday that Harris was "extremely off the mark" in criticizing the Barry administration's application for federal operating subsidies.

Glee said the city applied for the 1982 subsidy in a timely fashion but that a dispute between the city and HUD over the level of funding and the disposition of the public housing authority's long-standing debt resulted in a delay in HUD disbursing the funds.

Public housing authorities in major cities throughout the country have wrangled with HUD this year over subsidy funding levels. Although Congress has appropriated funds for the subsidy program, HUD has held back much of those funds.

"It's not just the D.C. housing authority facing that problem," explained a staff assistant to the House Banking, Finance and Urban Affairs Committee, which oversees the subsidy. "It's all of them."