District of Columbia officials, who last fall said the city faced a potential $110.4 million deficit for the year, said yesterday that a continued decline in spending should enable the city to complete fiscal 1983 with a balanced operating budget.

A third-quarter financial report released by the city yesterday showed that the $110 million budget gap predicted last November has now been narrowed to $14.5 million and continued savings are expected to reduce it to zero by Sept. 30, the end of the current fiscal year.

There was a $23 million drop in projected expenditures during the third quarter, which follows a $43.9 million reduction during the previous quarter.

"Careful management and close controls on expenditures will be necessary in the final quarter to eliminate the remaining $14.5 million, but the results of our third quarter assessment indicate that we are on course to achieve that goal," Mayor Marion Barry said.

City financial officials said that the $14.5 million is needed to help the city reduce its $296 million accumulated debt by $20 million this year, an amount that was mandated by Congress. Officials said the city already has set aside $5.5 million of the $20 million included in this year's budget.

Alphonse G. Hill, the city's deputy mayor for finance, said that he is pleased that revenue projections are holding firm, at $1.77 billion, while there is a continued downward trend in spending. The city's revised budget for the year is $1.78 billion. "We're trying to do everything on an even keel throughout the year" so there will not be drastic cuts in services, Hill said.

The Department of Human Services, one of the agencies originally cited as a major reason for the overspending, showed a $9.4 million reduction in projected spending during the third quarter. However, its expected expenditures are still running $4.5 million over the department's $336 million budget for the year, the highest amount of projected overspending by any city agency.

Meanwhile, next year's $2 billion city budget is awaiting final congressional approval after the differences between the House and Senate versions are worked out in a conference committee early this fall.