The D.C. government's revenue shortfall grew to $12.9 million last month, city officials reported yesterday, increasing the possibility that the city could have a budget deficit when the fiscal year ends Sept. 30.

In May, city revenues fell $16.2 million short of the amount forecast for the month and dipped $2.6 million below the level predicted for that point in the year. Mayor Marion Barry said then that the shortfall was a cyclical downturn in tax collections that probably would be nullified by June revenues.

The D.C. Department of Finance and Revenue reported yesterday, however, that June revenue collections were $7.6 million less than expected, driving the cumulative shortfall to nearly $13 million.

"I want to emphasize that these reports showing the shortfalls are our regular monthly reports," Barry, who had been briefed on the report earlier, said Tuesday. "There's no cause for alarm."

" City Administrator Elijah B. Rogers has already taken some initiatives, management initiatives to handle the problem," Barry said. "In a worst case situation we'll maybe have a $5 million or $6 million problem for the whole year. Six million dollars out of a $1.6 billion budget is not really a problem."

However, Philip M. Dearborn, a municipal finance specialist for the Greater Washington Research Center and former adviser to Barry, said a downturn in tax collections would be especially bad for Washington because it has no surplus from previous years.

"A $12 million shortfall is not a great amount as part of the budget," said Dearborn. "But D.C. is in trouble the minute it adds to its accumulated deficit.

"It's also a bad sign to have a shortfall now," he said. "It reverses the trend of revenues coming in over estimates that we were seeing at the end of last year and earlier this year. If the downtrend continues, the city budget will have a deficit."

In a report issued last week, D.C. Auditor Otis Troupe recommended that the city immediately begin cutting spending by $13 million in order to avoid a budget deficit. That proposal did not take into account the added shortfall of revenues revealed in the June revenue report. Troupe was not available for comment yesterday.

City Council member John A. Wilson (D-Ward 2), chairman of the council's Finance and Revenue Committee, predicted last week that the city would end the fiscal year with a deficit of $20 million to $40 million.

Wilson said yesterday that more shortfalls and continued overspending that he believes is taking place in city agencies could drive the figure higher.

Wilson said Barry has an unannounced hiring freeze in effect in the city government and is using money from the unpaid salaries to compensate for overspending.

Rogers, asked about a hiring freeze, said only that the city government is saving money by leaving positions vacant.

Wilson also said Barry withdrew his support Monday for a $36 million tax-relief package that would reduce the city's residential property-tax rate from $1.22 per $100 of assessed value to $1 and the commercial property-tax rate from $2.13 to $2.00.

The tax-relief package also included a 50 percent property-tax cut for persons over age 65 who earn under $8,000. The package is currently under consideration by Wilson's committee and was expected to be recommended for council action sometime before Sept. 30.

Barry's press secretary, Annette Samuels, said she does not know of any change in the administration's position on the tax.

Wilson, meanwhile, said that the downturn in city revenues has dampened his own support for the tax relief plan.

City Administrator Rogers said he does have a contingency savings plan. "We have a contingency plan. We've always had it, but I'm not ready to reveal it to you now.

"I'm telling you we are going to have a balanced budget or reduce the accumulated deficit," Rogers said. "I have it under control. You can count on it."

The June revenue report shows the city's tax revenues down in several key categories: sales and use taxes down $2.1 million for the month; individual income tax down $3.5 million; corporate franchise taxes down $1.4 million, and bank gross earnings taxes down $3.9 million.

The only area where tax revenues were higher than projections for the city last month was in selective sales and use taxes, such as the gas tax, where the taxes collected were $1.1 million over the anticipated income.

The revenue report also showed "slightly below estimate" tax income for water-sewer revenue and in revenues set aside for construction of the convention center. The report attributed the sewer-water tax shortfall to "late payments from Virginia for water services," and the convention center revenue shortfall to "weaknesses in the hotel occupancy tax."

The latter tax was set aside specifically to help finance the convention center. During the first five months of this year, hotel occupancy has been off more than 11 percent, with the number of hotel rooms filled at their lowest rate since 1946.

Last year, when the city finished the year with a $68 million surplus, the June revenue report showed the city with $18 million more than previously estimated.