Mayor Marion Barry, who six months ago warned that the D.C. government faced a potential $110.4 million deficit for the year, predicted yesterday that the city will complete fiscal 1983 with a balanced operating budget, including some money to reduce its massive accumulated debt.

Barry released a mid-year financial report indicating that the $110 million budget gap projected last fall has been narrowed to $37.6 million now and is expected to dwindle to zero by Sept. 30, the end of the fiscal year.

The sharp improvement is due to administrative cost-saving measures, pending increases in certain taxes, including the gross receipts tax on utilities, and a slight improvement in the economy, the mayor said at a press conference.

"A significant portion of our fiscal 1983 potential probem has been solved without layoffs or significant increases in taxes," Barry said, adding that the spending squeeze he ordered didn't result in an appreciable decrease in services or programs.

"I don't think citizens have suffered any program pain," he said. "I haven't heard of any complaints of program pain."

However, City Council member Polly Shackleton (D-Ward 3), chairman of the Human Services Committee, said yesterday she has received complaints from some advocate groups about reductions in home nursing and health service programs offered by the city.

"We really are not too sure of what social service programs have been cut," Shackleton said. "We've heard of some problems where there have been some cuts . . . We've requested a list of the cuts that have been made."

The mayor's announcement yesterday of a marked improvement in the city's budget picture is the latest in a series of reversals of financial fortune that have marked Barry's 4 1/2 years in office. Two years ago, for instance, Barry warned that the city might be headed for a $60 million deficit in fiscal 1981, but ended the year with a whopping $68.3 million surplus.

Last November, Barry told the D.C. City Council that the city would finish the current fiscal year with a $110.4 million deficit in the general fund unless agencies sharply cut back their rate of spending and the revenue picture improved.

The mayor said then that the potential budget gap consisted of $52.7 million in anticipated revenue shortfalls and $57.7 million in potential overspending by several major agencies, including the Department of Human Services, the Department of Housing and Community Development and the Department of Corrections.

The improved budget picture announced yesterday resulted from a net increase in projected tax revenues of $28.9 million and a net reduction of $43.9 million in projected overspending.

The city also expects to save an estimated $12 million to $13 million in Medicaid costs this year as the result of an agreement with 12 local hospitals to place a cap on total Medicaid reimbursements the hospitals may claim.

This year's budget includes $20 million insisted upon by Congress to help reduce the city's accumulated debt.

Alphonse G. Hill, deputy mayor for finance, warned earlier this year that the city might have to forgo making that payment because of pressing budgetary problems. Yesterday, Barry reaffirmed his intention of making that payment "to significantly reduce our accumulated general fund deficit."

The mayor released the up-beat mid-year report one day before Congress was scheduled to begin hearings on the city's fiscal 1984 budget.

Barry is hopeful that the report, forecasting a balanced D.C. operating budget for the third year in a row, will make congressmen more receptive to the 1984 budget proposal and to the mayor's latest plan for eliminating the city's $296 million accumulated debt.

"It better helps us to sell our case," Barry said.