Riggs National Bank and National Savings & Trust Co., two large Washington bank firms, reported yesterday that operating profits advanced sharply in the first nine months of 1978.

Earnings also were higher for Federal National Mortgage Association in both the third quarter and first nine months compared with the same periods last year, although third-quarter profits trailed second-quarter levels.

Nine-month profits of Riggs, the largest commercial bank organization in metropolitan Washington, rose 27 percent to 13.6 million ($4.50 a share) from $10.7 million ($3.55) in the same 1977 period.

For the third quarter alone, Rigg's profits advanced by a smiliar amount - 26 percent - to $5.07 million ($1.67) from $4.04 million ($1.33(.

Riggs Chairman Vincent C. Burke Jr. attributed the increases during 1978 to a higher volume of such earning assets as loans, coupled with higher interest rates.

Loan volume on Sept. 30 was a record $1.07 billion, up 22 percent from $882 million one year earlier. Rigg's deposits also increased sharply to $1.8 billion from $1.5 billion, a gain of 21 percent.

Although interest expanses rose 46 percent in the nine months to $51 million, reflecting payouts on savings instruments that have moved higher, interest income rose by 30 percent to $105 million and accounted for the overall gain in profitability.

The prime interest rate, that charged to the best corporate customers has been climbing steadily and now stands at 9 3/4 percent. Because of continued upward pressure on short-term interest rates, a 10 percent prime rate now is expected in the near future.

Earnings reported yesterday by Riggs also include results of its wholly owned Central Charge Service subsidiary, the largest regional credit card business.

National Savings & Trust Co. reported nine-month profits of $2.88 million ($6.29 a share), up more than 30 percent from $2.21 million ($4.83) in the same period last year.

Chairman Douglas R. Smith said income from all sources jumped to $25 million from $20 million, while deposits rose to $401 million on Sept. 30 from $320 million a year ago.

Directors of NS&T yesterday voted a regular quarterly dividend of 80 cents a share payable Nov. 1 to stockholders of record Oct. 20.

Federal National Mortgage, another company whose profits are sensitive to interest rate fluctuations, reported third-quarter earnings of $47.2 million (79 cents a share) compared with $37 million (62 cents) in the same period last year.

Nine-month profits rose to $158 million ($2.63 a share) from $121 million ($2.04) in the 1977 period.

Although the Washington company's results show increases over last year, third-quarter profits were down from $58.7 million (97 cents) earned in the second quarter of 1978.

Fannie Mae provides a secondary market for home mortgages and thus aids the housing markets during periods of tight money.

The quarter-to-quarter decline reflected a drop in commitment fees and other income to $13.9 million from $38.5 million in the abnormally active second quarter, Fannie Mae said.

FNMA made commitments to purchase mortgages totaling $2.3 billion in the third period compared with a record $7.1 billion during the previous three months.