First Virginia Banks Inc. yesterday reported a 13 percent increase in earnings for the third quarter ending Sept. 30.

Net income was $14.5 million (71 cents per share), compared with $12.8 million (63 cents) in the third quarter last year. The income figures for 1986 have been restated to include four banking organizations acquired during 1987.

For the nine months, net income was $42.5 million ($2.08), compared with $38.6 million ($1.91) for the same period the previous year.

On Sept. 30, total deposits were $3.8 billion, up from $3.6 billion in the previous September. MNC Financial of Baltimore, formerly Maryland National Corp., reported yesterday a 26 percent increase in profits for its third quarter.

MNC, whoses subsidiaries include Washington's American Security Bank, said its net income was $40.1 million ($1.34) for the quarter ending Sept. 30, compared with $31.8 million ($1.08) for the same period the previous year.

For the nine months, net income was $105.3 million ($3.54), compared with $90.3 million ($3.08) for the same period the previous year.

As of Sept. 30, MNC had total deposits of $10.5 billion, up 17 percent from the same date in the previous year