Two of Washington's largest banks announced substantial increases in earnings during the third quarter, while the third-largest District bank, the National Bank of Washington, reported an 11 percent decline in earnings.

Riggs National Corp., parent of the District's largest bank, Riggs National Bank of Washington, reported an earnings increase of 20 percent compared with the same quarter last year, and American Security Corp., parent of the second-largest bank, American Security Bank, reported a 43 percent increase.

*American Security Corp. posted a $7 million (60 cents per share) profit, compared with a $4.9 million (43 cents) profit for the same period last year.

The company attributed much of the improvement to a $5.9 million increase in net interest revenue and a $4 million decrease in the company's loan-loss provisions.

For the first nine months of the year, American Security earned $19 million ($1.63), up 14 percent from last year, when the company earned $16.7 million ($1.46) during the first nine months.

The bank's assets as of Sept. 30, 1985, totaled $3.98 billion, up from $3.84 billion a year ago.

*Washington Bancorporation, parent company of the National Bank of Washington, reported third-quarter earnings of $2.4 million ($1.71 per share), down from $2.7 million ($1.93) for the same period last year.

For the first nine months, the company reported profits of $7 million ($5.06), down 11 percent from $7.9 million ($5.77) in 1984.

Luther H. Hodges Jr., chairman of NBW, attributed the decline to increased allowances for expected loan losses. But he predicted fourth-quarter and year-end results will exceed those of last year.

Additions to the loan-loss reserve in the third quarter were $2.9 million compared with $1.1 million a year ago.

*Riggs National Corp. said net income for the third quarter ending Sept. 30 climbed 20 percent to $8.15 million ($1.36 per share), compared with $6.79 million ($1.13) during the same period last year.

Net income for the first nine months rose 16.5 percent to $23.7 million ($3.96), compared with $20.35 million ($3.40) during the same period in 1984.

At the end of the third quarter, assets were up 8.5 percent to $5.16 billion, loans and deposits were both up more than 20 percent and non-performing assets of $15.9 million were down nearly 40 percent, compared with Sept. 30, 1984.

*Citizens Bancorp., the holding company which operates Citizens Bank & Trust Co. of Maryland, reported that its net income for the third quarter climbed 21 percent to $5.78 million ($2.77), compared with $4.79 million ($2.30) for the same period last year.

Net income for the first nine months rose 21 percent to $16.7 million ($8.03), compared with $13.9 million ($6.70) for the first nine months of last year.

*The Student Loan Marketing Association (Sallie Mae) reported net income of $31.3 million (63 cents) for the third quarter, up 19 percent over profits of $26.3 million (50 cents) last year.

Sallie Mae, a federally chartered, stockholder-owned corporation, buys insured student loans and provides other financial services to financial and educational institutions participating in the guaranteed student loan program.

Sallie Mae's earnings growth "continues to reflect strong asset acquisition, attractively priced financings and increased operational efficiences," said Edward A. Fox, president and chief executive officer.

At Sept. 30, the corporation's total assets stood at $13.6 billion.