Families supported by public welfare programs in the Washington area fell far behind financially during the decade of the 1970s, according to a new study made public today.

From 1970 to 1978, while the cost of living went up 68 percent, welfare payments needed to provide food and shelter rose by only 13 percent, the Greater Washington Research Center reported.

The decline came as the actual number of welfare recipients in the region declined by 15,884 between 1975 and 1978, reversing a sharp uptrend in the first half of the decade.

In 1978, a total of 151,008 persons in the metropolitan area were supported by the two largest welfare programs -- aid for families with dependent children, and general public assistance. Of those, 101,007 were in the District of Columbia.

According to the new study, the average welfare family in the region in 1970 received a monthly payment of $203. By 1978, with the consumer price index up 68 percent, the average payment had increased only 13 percent, to $230, the study reported.

Janice Hamilton Outtz, who prepared the 17-page study from official statistics, said the loss of family buying power came because mothers on welfare are having fewer children who qualify for payments and because financially pressed governments are not increasing benefit levels.

A result is that the plight of welfare-supported families is becoming desperate, according to a lawyer whose public-interest agency represents many welfare clients.

"Even if the lower-income people were getting more money if they could qualify for (public assistance) they were falling farther below the poverty line," Lynn E. Cunningham of Neighborhood Legal Services said. "Our lawyers see it every day. It is very hard to know what to do."

Outtz, a researcher formerly on the staff of Howard University, said the average annual benefits in cash and food stamps in 1978 was $5,100 to four-member families supported under the program of aid to families with dependent children.

That figure was only 59 percent of the adjusted figure of $8,685 that the U.S. Bureau of Labor Statistics estimated a welfare-supported family of four would need in Metropolitan Washington to live on a low budget. A nonwelfare family would need another $3,713 -- a total of $12,398 -- for taxes and health care costs, according to the bureau.

District recipients got a 5 percent cost-of-living increase last year. Mayor Marion Barry originally proposed another 5 percent rise in the budget he sent to Congress for the fiscal year starting Oct. 1.

However, as a cost-cutting move designed to avert a deficit, Barry cancelled that proposed increase in an amended budget he recently submitted to the D.C. City Council. The council approved the reduced budget last week and sent it along to Congress.

For the metropolitan area, welfare costs in 1978 totaled more than $144 million in state and local funds. Of that figure, the District's share was $103 million.

The regional welfare case load increased 16 percent in the first half of the decade of the 1970s largely because of changed national eligibility standards, but then declined 9.5 percent between 1975 and 1978, Outtz found.

One reason, she said, was a drop in the size of families supported by welfare. In 1970, the average welfare family was made up of four persons, compared with a family average of 3.1 in the general population. By 1977, the average welfare family had dropped to three persons while the average in the general population was 2.8 persons.

Although the Outtz report did not speculate on the reasons for the decline in family size, one apparent possibility is the availability of publicly financed abortions under the Medicaid program that serves welfare recipients.

The report found that the District of Columbia's dominant share of all regional welfare recipients changed only slightly during the eight-year period. rWith about 20 percent of the region's population, the District had 66 percent of all recipients in 1970 and 67 percent in 1978.

[In 1970, the District had 41,787 of the region's caseload of 63,189. In 1978, the city had 59,220 of a regional total of 87,819.]

Suburban Maryland's 24 percent share in 1970, a total of 15,375 persons had declined to 21 percent of the regional total. But because of population growth, the actual number of people on the rolls increased slightly, to 16,963.

Northern Virginia's 10 percent share in 1970, a total of 6,027 persons, rose by 1978 to 12 percent, or 11,636 persons.

By far the largest proportionate increase in the regional caseload -- from 770 to 4,107 persons, a rise of 550 percent in eight years -- occurred in Alexandria. This compared with 139 percent regionally and nearly 142 percent for the District.

Payments by household and by individual recipients vary significantly within the region but, according to Outtz, did not cause many families to move in order to gain higher payments.

For the metropolitan area, the average monthly payment per household in 1978 was $230 a month. That ranged from a high of $240 in the District to a low of $173 in Virginia's Loudoun County. The average for suburban Maryland was $199 and in Northern Virginia it was $230.

Payments to individual recipients averaged $78 for the region in 1978, with the range from $88 in Arlington County to $60 in Maryland's Charles County. The District payment was $81, while the average for suburban Maryland was $69 and in Northern Virginia it was $83.