Construction of federally subsidized housing units for the Washington area has been reduced by 20 percent because of President Reagan's cuts in the federal housing program, according to figures released yesterday by the Metropolitan Washington Council of Governments and federal housing officials.

The figures, the first to translate the budget reductions into reduced housing for low- and moderate-income families, show that instead of receiving $12.5 million to finance 1,886 housing units as the Carter administration had projected, area governments from Bowie to Washington to Loudoun County will share only $10.3 million or 1,514 units for public and subsidized rental housing.

The District will receive the largest number of units, but also suffer the greatest reduction -- 30 percent. The city will receive 496 units instead of the projected 633.

But some area jurisdictions, such as Montgomery and Prince George's counties, have been cushioned from feeling the full impact of the cutbacks because they will receive part of the 275 extra subsidized units that area was awarded last year by the federal government. The additional units were a reward for the cooperative system the 16 local jurisdictions used to divide up the area's subsidized units.

"This is definitely not good news," said Ruth Crone, director of human resources and public safety at COG. "Clearly we will be getting substantially fewer units than we had hoped for. But we are fortunate that because of the cooperative effort we have the bonus units and they will help plug up some of the losses."

Pat Maier of the Montgomery County Department of Housing and Community Development said the cutback will "severely affect" that county's moderately priced dwelling unit program.

That program, the only of its kind in the area, requires developers to price 15 percent of the homes in all new developments for sale to moderate-income families. Then, using its subsidy funds, the county has assisted people with low incomes -- less than $21,600 a year for a family of four -- in buying some of the homes.

There are 7,000 families waiting for subsidized housing in the District; 6,000 people in Montgomery, which will receive 105 subsidized units and 1,500 people in Prince George's, which will receive 125 new units. These counties will also receive some bonus units that area as of yet unallocated. Fairfax County with 1,800 waiting for subsidized housing, will get 321 new units.

The cutbacks come at a time when the construction of subsidized housing is the area's only source of new apartments. High interest rates have virtually halted the building of privately financed apartments.

"This is the one resource we had depended on for new housing and now that has been cut," said Crone.