Criterion Insurance Co. reported yesterday an increase in earnings for the third quarter of 1979, rebounding from depressed profitability early in the year.

Profits totaled $1.7 million ($1.17 a share) in the July-September period compared with $1.4 million (96 cents) from operations in the same period last year. A tax benefit equal to 18 cents a share in the 1978 period brought net income that year to $1.66 million.

For the first nine months, the Washington auto insurer reported earnings of $3.77 millon ($2.58) compared with $3.8 million ($2.61), not counting the tax benefits, which added 50 cents a share and brought net income to $4.5 million ($3.11) in the 1978 period.

First American Bank of Virginia announced profits for the third quarter of $2.4 million ($1.51). For the first three quarters, net income for First American, based in McLean was $6.1 million, a 28 percent increase over the bank's $4.8 million for 1978.

Acacia Mutual Life Insurance Co. of the District reported sales of $406 million for the first nine months of the year, an increase of 12.3 percent over the first nine months of last year.

Acacia's assets rose during the first three quarters to a new high of $780.9 million, up from $755.4 million at the begining of the year.

C.A.C.I. Inc. reported profits of $363,319 (35 cents) for the third quarter of 1979, an increase of 64 percent over the company's profits of $221,040 (21 cents) a year ago.

The research, management and computer company, based in Arlington, reported a 71 percent increase in revenues for the quarter. The company's revenues for the third quarter jumped to $6.5 million over $3.8 million for the same period in 1978.

National Bank of Washington's net income increased to $1.76 million ($1.28 a share) from $1.34 million (98 cents), a 34 percent gain. Income before securities transactions increased to $1.76 million ($1.28) from $1.56 million ($1.14).

For the nine months, NBW reported income before securities dealings of $4.79 million ($3.49), up from $4.51 million ($3.28) and net income of $4.79 million (3.49) up from $4.28 million ($3.12).

Bank of Columbia N.A. showed income before securities transactions of $254,000 (58 cents) for the first nine months of the year, up 120 percent from the $115,000 (26 cents) earned a year ago.

Metropolitan Federal Savings and Loan Assn. of Bethesda reported its earnings fell by 11 percent for the third quarter, depressing profits for the first nine months by 4.1 percent.

Metropolitan declared its regular cash dividend of 12.5 cents per share, payable Oct. 10 to shareholders as of Sept. 30.

Metropolitan Federal reported profits of $536,000 ($1.20 per share) for the quarter, down from $605,000 ($1.35) a year ago. For the first nine months of the year, earnings were $1.63 million ($3.63) down from $1.69 million ($3.78).