The most recent internal financial review of the D.C. Department of Human Services shows the agency, the city government's largest, overspending its budget by $11 million through June 30.

Until now, Mayor Marion Barry's administration has indicated that the city's budget problems this year are connected to a shortfall of tax revenues. The DHS report provides the first concrete indication of a separate problem of overspending.

Barry administration officials maintain that the overspending will be eliminated and that an eventual $3 million surplus, as previously promised by Barry, will indeed materialize by the time the fiscal year ends on Sept. 30.

The report on DHS overspending, distributed privately to city officials late last month, shows the agency $7 million over its budget for salaries and $4 million over budget in its purchases of supplies and fuel and its payments for rent.

City budget director Gladys W. Mack said Friday night that the Barry administration sticks by its prediction of a surplus, and said the figures cited by the mayor in announcing the expected surplus were not intended to spell out individual spending problems various departments might have had. The departments, she said, have been told to correct the problems.

In predicting the surplus, Barry said the city government faced a potential deficit of $5 million due to lagging revenues, and pledged to implement an $8 million savings program, which would finally produce a $3 million surplus. He gave no description of agency spending patterns.

"Agencies that have forecast spending less than their budget, we have told to hold to that forecast," Mack said. "Agencies that have forecast overspending, we have told to bring their budget in line. We are focusing on the end of the year, and we will have a surplus."

Critics of the Barry administration's financial policies, such as City Council Finance Committee Chairman John A. Wilson (D-Ward 2), have said they suspect a widespread spending problem but say they have been frustrated by the administration's decision not to release data on spending. Wilson has predicted a deficit of $20 million to $40 million for the year, but acknowledges that his forecast is not based on official data.

In addition, say Wilson and other critics, the city's computerized Financial Management System has not been updated with current figures. DHS, for example, is shown in the computer to have no deficit.

James E. Buford, director of DHS, said the department has a plan to erase the $11 million potential deficit. He said DHS hopes to save $7 million before the end of the fiscal year through limits of hiring and purchases.

"We don't have a hiring freeze on, but we are hiring only for ciritically necessary positions -- nurses, physicians, data processing," Buford said. "We have staff in all the positions required to remain certified for federal funds."

Robert Boyle, the agency's controller, said new restrictions have been placed on purchasing, which will curtail sharply buying for the rest of the fiscal year.

The remaining $4 million spending problem, according to the DHS officials, will be solved by increased billing of the federal government for the cost of administering the Medicaid, Aid to Families with Dependent Children and food stamp programs -- expected to produce $2 million -- and by audits of hospitals that accept Medicaid patients, another anticipated $2 million.

If all the savings materialize, Boyle said, the department, which has a $500 million budget, should end the year with a surplus of $500,000. "Obviously there is an error factor there, but that is our best estimate at this point," Boyle said.

A deficit of the magnitude cited by Barry's critics would be quite small compared with the city government's overall budget of nearly $2 billion. However, the city is sensitive about the handling of its finances because it already has a $309 million accumulated debt and does not want to further damage its chances of entering the municipal bond market.