Riggs National Corp., which controls Washington's largest bank, yesterday reported a 2.8 percent decline in second-quarter net income because of a large increase in problem loans.

Riggs said that so-called nonperforming assets--essentially past-due loans, loans on which the terms have been renegotiated and real estate that was foreclosed on--grew 22 percent in the first half of the year. Riggs said it had $78.7 million of nonperforming assets on June 30 compared with $64.3 million at the end of last year.

Nonperforming loans were 4.6 percent of Riggs' total loan portfolio of $1.7 billion, according to figures supplied by the bank. While the worldwide recession and the four-year spate of high interest rates are pushing up problem loan totals at nearly all banks, Riggs has a higher portion of problem loans than most.

However, the bank said that most of its so-called problem loans are "well-secured by real estate and the bank does not anticipate losses of any consequence in this loan category."

In 1981 Riggs' problem loans grew from less than $20 million to $64.3 million because of a sharp increase in nonperforming foreign loans and real estate loans. Most nonperforming loans do not actually become write-offs, or loans the bank decides never will be repaid. Furthermore, even after a bank writes off a loan as uncollectible, it often recovers all or part of the credit.

Riggs reported second-quarter income of $6.39 million ($1.07 a share) compared with $6.58 million ($1.10) during the three months ended June 30, 1981. Riggs had no gains or losses on securities transactions.

For the first half of the year, income was up 4.8 percent to $12.66 million from $12.08 million on June 30, 1981.

The bank holding company, with total deposits of $3.1 billion and total assets of $3.6 billion on June 30, also cited unspecified extraordinary costs of a "nonrecurring nature" as playing part of the role in the second-quarter decline in net income.

The bank said it anticipated the increase in nonperforming loans, calling the income performance for the quarter and the first half "ahead of the budget plan." In a release, the bank noted the "current economic pressures on the real estate construction industry in the Washington, D.C., area."

Riggs is a major lender to real estate developers.

Virginia National Bankshares Inc., which owns the state's second-largest bank, reported yesterday that second-quarter income before gains or losses on securities transactions was $8.15 million ($1.10 a share), 6.7 percent higher than the $7.64 million ($1.07) it earned in the second quarter of 1981.

After securities losses, the bank's net income was $8.06 million compared with $6.87 million during the first quarter of 1981.

Virginia National had $3.28 billion in assets on June 30, an increase of 15.6 percent over June 30, 1981. Its deposits were $2.569 billion, 15.5 percent more than the $2.24 billion of deposits the year before.

For the first half, Virginia National's net income before securities transactions was $15.53 million, 4.6 percent higher than the $14.85 million the bank holding company earned in the first half of last year.

Student Loan Marketing Association reported second-quarter net income of $8.9 million ($8.91 a share), 140 percent more than the $3.7 million ($3.71) it earned in the same period last year. Sallie Mae, as the association usually is called, purchases insured loans made under the Guaranteed Student Loan Program and the Health Education Assistance Program. For the first half of the year, Sallie Mae earned $16.5 million, a 117 percent increase over the $7.6 million it earned during the first six months of 1981.

The association had assets of $6.1 billion on June 30, 54 percent more than the $3.9 billion it had on June 30, 1981.