The three biggest banks in the District of Columbia, Virginia and Maryland reported record second quarter profits yesterday.

Earnings increased 27.1 percent at Virginia National Bankshares Inc., 28 percent at Maryland National Corp. and 34.8 percent at Riggs National Bank.

Executives of all three banks said high interest rates were the main reason for the dramatic jump in bank profits.

But W. Wright Harrison, chairman of the board of Virginia National, warned that, "A continuation of this trend may be difficult to sustain under anticipated enconomic conditions."

Riggs' profits for the quarter ended June 30 increased by $1.48 million to $5.74. million. For the first half of the year Riggs' net income was up 30.3 percent to $11.15 million ($3.68 per share.) Riggs had no gains or losses from securities transcations to effect its earnings either this year or last.

Maryland National Corp. -- the holding company parent of Maryland National Bank -- showed second quarter earnings before securities transactions of $6.8 million (96 cents per share) up from $5.4 million (75 cents) a year earlier. Net income for the quarter was $6.4 million, up from $5.3 million.

For the first half, Maryland National reported earnings before securities transactions of $13.5 million ($1.90 per share) and net income of $12.6 million, up from $10.7 million (1.50) and $10.6 million net a year ago.

Virgina National reported income before securites transactions for the quarter of $5.03 million (75 cents) -- up from $3.96 million (59 cents) last year. Net income increased to $4.78 million from $3.93 million.

For the first six months of 1979 Virginia National earned $10.2 million ($1.51 per share) before securities transactions and a net of $10.17 million. A year earlier income before securities transactions was $7.75 million (1.15) and the net was $10.17 million.

Comparing the three biggest local financial institutions in size as of June 30 shows Maryland National is the largest, with assests of $3.1 billion, deposits of $2.2 billion and loans of $1.9 billion. Virginia National is second with assets of $2.48 billion, deposits of $2.03 billion and loans of $1.49 billion. Riggs reported assets of $2.26 billion, deposits of $1.89 billion and loans of $1.13 billion.

Federal National Mortgage Association, a Washington company that supports a secondary market in home mortgages, reported a sharp decline in second-quarter profits. Soaring interest rate costs helped to trim earnings to $40 million (67 cents a share) compared with $59 million (97 cents) a year ago.

Six-month earnings were down to $79 million ($1.32 a share) from $111 million ($1.84) on the first half of 1978.

First Virginia Banks Inc. of Falls Church, reported yesterday record earnings for the second quarter of 1979 -- the 16th consecutive quarter in which earnings exceeded those of the comparable quarter the previous year.

The company reported profits of $3.6 million (35 cents a share), a 24 percent increase over $2.9 million (28 cents a share) for the second quarter last year.

For the first six months this year net income including securities gains and losses was $6.6 million (63 cents a share), a 19 percent increase over the $5.6 million (53 cents a share) for the same period last year.

Thomas K. Malone Jr., chairman of the board and chief executive officer, said the company had high earnings because it was able to meet the strong loan demand and deposits increased. Malone added that while earnings are expected to remain high through the remainder of the year, they will not increase at the same rate experienced during the first six months if an economic slowdown develops.

At the end of June, the holding company banks had total deposits of $1.3 billion.

Wards Company, Inc., a Richmondbased national audio, television and appliance merchandiser, reported earnings for the three months ending May 31 of $380,000 (51 cents a share) compare to $359.00 (47 cents a share) for the comprable period last year.

Wards operates Circuit City equipment outlets in the Washington area. Sales in the quarter rose 6 percent to $24 million.