Profits of Riggs National Bank and its Central Charge Service subsidiary soared nearly 34 percent in the first quarter of 1978, the Washington bank company reported yesterday.

Operatings earnings and net income amounted to $4.3 million ($1.42 a share) compared with $3.2 million ($1.06) in the same quarter of 1977, with no securities gains or losses in either period.

Chairman Vincent C. Burke Jr. attributed the increased earnings to greater interest income from higher yielding loans and investment securities, offset partially by additional operating expenses.

Riggs loan volume totaled $925 million on March 31, up 15 percent in the past 12 months.Deposits increased 13.5 percent to a record $1.75 billion and total resources climbed 18 percent to $2.07 billion.

First American Bank of Virginia, based in McLean, reported first-quarter operating profits of $1.44 million (91 cents a share) compared with $1.28 million (80 cents) in the same period last year, assuming that the bank had been in operation at that time.

The bank, now the largest in Northern Virginia and fourth largest in the D.C. area, was formed March 31 with the merger of three Financial General Bankshares institutions - Alexandria National Arlington Trust and Clarendon Bank Trust.

Deposits of First American on March 31 were $624 million compared with $572 million for the three banks a year earlier.

Metropolitan Federal Savings and Loan Association, of Bethesda, reported a 52 percent increase in profits for the first quarter. Net income was $548,765 ($1.29 a share) compared with $361,430 (90 cents) in the same period last year.

President Jessie Hilderbrand said assets rose 20.5 percent to a record $219 million and savings rose 14 percent to $185 million on March 31 compared with 12 months earlier.

A cash payout of 12 1/2 cents a share will be paid April 5 to stockholders of record March 31.