The population of the District of Columbia dropped by more than 100,000 during the last decade and is now at its lowest since the 1930s, Census results released yesterday.

The results, attributed primarily to a decline in the size of the average household in the city, confirm earlier indications that the nation's capital is becoming more and more a city of single adults and childless couples and less a city of families with children.

The apparent decline in population could also forecast a loss to the District government of millions of dollars in federal aid that is calculated on the basis of census results, and top city officials said yesterday they are considering asking for a recount.

Preliminary calculations released yesterday put the population of the city at 568,300 as of last April.

That figure is far lower than estimates made by the city government and by the Census Bureau itself over the last two years, and District officials characterized it as "erroneously low and obsolete" and "inherently not credible."

Mayor Marion Barry, in a letter to Census Bureau director Vincent P. Barabba, said that Census Bureau field workers here already have found "about 70,000" more persons since the initial calculation was made. Barry said he would "consider an official request for a recount" if further checks fail to bring the official results closer to higher figures claimed by District demographers.

If Barry's information is correct, it would put the city's total population at 638,267 -- the lowest 10-year figure since 1940 and a decline of 15.6 percent from the 1940 figure of 756,500. The population has not been below 600,000 since the 1930s.

David Levine, deputy director of the Census Bureau, said in a telephone interview that it was "fully logical to expect that final numbers would be somewhat higher" than the preliminary figure.

He said that the preliminary results were given to the District government in the expectation that they would be refined upward as city officials review them and "point out errors or suggest we missed certain areas."

That reflects a procedure adopted for the first time this year, in which the Census Bureau has delivered its raw preliminary findings to some 39,000 local governments and invited them to participate in refining the figures.

"This is a cooperative effort, not an adversary proceeding," a Census Bureau spokesman said yesterday.

Preliminary figures for the suburbs, released earlier, showed similar but not as drastic declines in overall population and household size in the older, inner suburbs such as Falls Church, Arlington and Alexandria. Sharp increases have occurred in outliving areas such as Charles and Loudoun countries.

The census results are of critical importance to local government because they are used in determining the amount of federal aid in some 125 programs ranging from welfare to highway safety.

New York officials calculate that each resident counted is worth $200 in federal aid to the city, and while Levine said that figure was "very risky," it is clear that millions of dollars ride on the outcome.

"A correct count is of the greatest importance," Barry said in his letter to Barabba, "because it affects the number and size of federal grants for housing, jobs and other crucial programs, as well as the amount of District budget funds appropriated by Congress. In a fine of fiscal stringency. a correct count is essential to our ability to provide necessary services of all kinds."

He said that if "the efforts of our two staffs disclose serious problems remaining as to the technical adequacy of the local enumeration, I will consider an official request for a recount in the District of Columbia."

That would be in line with a resolution of the U.S. Conference of Mayors urging the Census Bureau to adjust its findings to take account of citydwellers the mayors believe were overlooked in the April count.

District officials, like those in other large industrial cities, said that the persons allegedly overlooked tend to be the ones most in need of the federal aid that would be reduced becauser of the short count: the poor, blacks, Hispanics and illegal immigrants.

The preliminary figures do not include any information about race or income. They are just unedited, unanalyzed data on numbers of people and numbers of households.

For the District, the figures show a population of 568,300 in 258,400 households. That is 2.1 persons per household, down from the 1970 figure of 2.72, and down from previous Census Bureau and District estimates of 2.42.

"This sudden acceleration in the decline of household size is inherently not credible," Albert Mindlin, the District's chief statistician, said in a memo to Barry.

Some decline in household size, reflected in the declining public school enrollment, is taken for granted, but not anything this drastic.

Mindlin's memo said preliminary results in 25 census tracts showed populations less than two-thirds of the estimates by the city government in 1968, leading to a "high suspicion of undercount."

It also questioned the number of persons found to be living in "group quarters," or institutions.

The census tracts covering Walter Reed Hospital, Gallaudet, College and the Catholic convents and monasteries of Brookland, for example, were found to have a total population of zero this year. They had 3,592 residents in the 1970 census. Only 160 residents were found at Georgetown and Catholic universities, down from 3,765 in 1970.

"In group quarters, their records are generally excellent," said Levine, and "it's very logical to assume" that some persons had been missed.

Levine said he knew that some of the 22,300 dwelling units found to be vacant actually were occupied and that these occupants eventually would be found and tabulated.