Marriott Corp. and First Virginia Bank reported higher profits yesterday, with the bank crediting high interest rates for the gains and Marriott blaming economic conditions for holding down its earnings.

But United Virginia Bankshares Inc. said its profits for the first three months of the year slipped because of losses on securities transactions, Federal National Mortgage Association reported it has cut its recent losses, and CACI Inc., an Arlington computer company, said its annual profits doubled last year.

Marriott's net climbed 18 percent to $16.9 million (63 cents a share) from $14.4 (54 cents), while revenues increased 24 percent to $516.2 million from $412.5 million in the first quarter of 1981.

Restaurant profits were down, food service earnings were flat and other operations were hurt by the harsh January weather and "strong competitive conditions due to continued economic softness," said President J.W. Marriott Jr.

Richmond-based United Virginia Bank recorded an 18 percent gain in assets over a year ago to $4.025 billion, but net income for the quarter slipped to $10.1 million ($1.77) from $10.3 ($1.92). Income before securities transactions was $11.1 million, a record high.

First Virginia Bank of Falls Church reported first-quarter earnings of $5.3 million (44 cents), up 16 percent from $4.6 million (38 cents) in the same period a year ago. Assets of the banks were up 8 percent to $1.8 billion.

CACI reported earnings of $2.6 million ($2.60 a share) for the nine months ended March 31, double the $1.3 million ($1.28) of the same period a year earlier. Revenues climbed to $66 million from $39 million for the CACI group of computer companies.

For the latest quarter, CACI earned just over $1 million (98 cents) on revenues of $25.6 million, up from $471,000 (45 cents) on revenues of $14.9 million.

FNMA--popularly known as Fannie Mae--said that losses declined for the second quarter in a row. The deficit was $42.8 million compared with a loss of $70.7 million in the first quarter of 1980. $