Large banking companies in the Washington region reported generally strong earnings increases yesterday, while Federal National Mortgage Association and Reynolds Metals Co. said recent interest costs or foreign exchange transactions caused profits to fall in the thrid quarter.

American Security Corp., Maryland National Corp., Virginia National Bankshares, Citizens Bank & Trust of Maryland and National Saving & Trust of Washington all reported higher profits.

Some of the bank earnings gains were less than for previous quarters of this year, however, as higher earnings from heavy loan volumes has been somewhat offset by higher money costs.

American Security, parent firm of the second-largest D.C. bank, said thrid-quarter profits rose to $5.6 million ($1.55 a share) from $5.2 million ($1.43) a year ago. Nine-month earnings were up 11 percent to $15.5 million ($4.25) from $14 million ($3.82).

Loan volume averaged $1.2 billion in the first nine months, a gain of $240 millionn from the 1978 period, as total assets increased by $300 million to $2.2 billion.

Maryland National, holding company for that state's largest bank, reported nine-month profits of $20 million ($2.81), up 24 percent from $16 million ($2.26) a year earlier.Third-quarter earnings rose 20 percent to $6.5 million (91 cents) vs. $5.4 million (76 cents). The results do not include gains or losses from selling securities.

Chairman Robert D. H. Harvey said that, in addition to higher earnings from loans, nonbank subsidiaries posted record earnings for the recent nine months.

Virginia National Bankshares of Norfolk said third-quarter profits before securities transactions rose 8 percent to $5.4 million (79 cents) from $5 million (74 cents). Nine-month operating earnings rose 22 percent to $15.6 million ($2.30) from $12.8 million ($1.89).

National Savings & Trust Co. reported nine-month earnings of $3.25 million ($7.11) vs $2.88 million ($6.29) and directors also approved a quarterly payout of $1 a share on Nov. 1 to owners of record Oct. 19.

Citizens Bank & Trust said nine-month earnings rose 20 percent to $7.35 million ($5.47) vs. $6.1 million ($4.54).

Federal National Mortage Association earned $45.3 million (74 cents) in the recent quarter compared with $47.2 million (79 cents) a year ago. Nine-month profits fell to $124.7 million ($2.06) from $157.9 million ($2.63), reflecting higher borrowing costs.

Reynolds Metal Co. earned $35 million ($1.82) in the third quarter compared with $46.6 million ($2.44) a year ago as sales rose to $829 million from $733 million. Chairman David Reynolds said foreign currency exchange losses and start-up costs for a plant in Corpus Christi, Tex., caused the reduction. But nine-month profits rose to $133 million ($6.94 from $78 million ($4.12) as sales rose to $2.5 billion from $2.1 billion.