Three more Washington banks reported yesterday that their profits increased sharply last year, reflecting higher interest rates and the healthy local conomy.

American Security Corp. turned in a 10 percent gain in earnings to $19.4 million ($5.30 a share), making American Security Bank the most profitabvle financial institution in the District of Columbia.

The biggest increase in earnings reported so far by local banks is at District of Columbia National Bank, which yesterday said its profits jumped 51 percent to $689,000 ($3.54 a share from $456,000 ($2.28).

And Union First National Bank of Washington turned in a 34.6 percent gain in earnings before securities losses to $5.4 million ($2.41 a share) from just over $4 million ($1.79).

As interest rates increased last year, most local banks improved their profit margains, with Madison National Bank up 44 percent, National Savings and Trust up 24 percent, First American Bank of Virginia up 12 percent and First National of Southern Maryland up 19 percent.

American Security's net of $19.4 million ($5.30 a share) compared with earnings of $17.6 million ($4.83) the prior year. Before securities transactions, the company earned $5.29 in 1978 and $4.72 in 1977.

For the fourth quarter, American Security reported earning of $5.5 million ($1.48), up from $4.4 million ($1.22) the same period a year ago.

American Security Chairman Carleton M. Stewart said consumer and corporate loans increased substantially in the metropolitan area, and national and international business loans also grew. Real estate lending increased to record levels, and American Security became the biggest mortageg lender in Washington, mostly due to the resurgence of construction downtown.

D.C. National's new president, Thomas S. Condit, attributed his bank's increased profits fo "the bullish downtown economic picture."

New income at wd.c. n/ational increased to $656,000 ($3.28 a share) from $480,000 ($2.40).Assets increased 22 percent to $89.9 million from $73.8 million, and depostits grew to $83.2 million from $68.8 million.

Condit, who was promoted from executive vice president to president last month, said 1978 saw the best growth in the bank's 16-year history, noting that the 51 percent growth in profits was the best performance among the District's eight largest banks. D.C. National ranks eighth on that list.

Union First reported net income for the year of $5.4 million ($2.38), up from $4.1 million ($1.81), a 31 percent increase. The Financial General bank's assets increased 9 percent to $640 million, deposits were up 8.6 percent to $461 million and loans grew 18 percent to $312 million.

For the fourth quarter, Union First earned $1.5 million (67 cents) before securities transactions, up from $1.1 million (48 cents). Quarterly net results were virtually the same.