Profits continued at record levels in the second quarter for Martin Marietta Corp., a large industrial firm based in Bethesda, and at Financial General Bankshares, the companies reported yesterday.

Earnings of Potomac Electric Power Co., meanwhile, rebounded modestyly in the second quarter but still trailed 1978 levels for the first six months of the year.

Martin Marietta, a diversified aerospace chemicals, aluminum, cement and construction materials company, said profits soared about 47 percent to $53.9 million ($2.15 a share) in the recent thre months compared with $36.8 million ($1.54) a year ago.

Sales advanced by more than 17 percent to $524 million for the largest industrial firm based for the largest industrial firm based in the D.C. area.

Chairman J. Donald Rauth, who has been bullish all year about his firm's business prospects, said yesterday that each of Marietta's five major divisions contributed to higher sales and profits.

"...Both out quarterly and midyear results are in overall accord with our expectations. We have advised our shareholders that Martin Marietta results for the full year probably will surpass all prior years. This continues to be our expectation," Rauth stated.

For the first six months, earnings were were a record $87 million ($3.44 a share) compared with $55 million ($2.29) a year ago. Sales rose to $961 million from $794 million in the 1978 period.

Financial General Bankshares. Washington banking firm that owns Union First of D.C. and First American banks in Maryland and Virginia, reported record second-quarter operating profits of $4 million (62 cents compared with $3 million (46 cents) a year ago.

Six-months earnings, also not counting securities gains or losses, rose to a record $7.3 million ($1.10) from $5.8 million (88 cents), a gain of 23 percent.

J. William Middendorf II, president of the bank holding company, attributed the record results to a 15.6 percent increase in net interest income from strong loan volume - particularly in consumer-related and commercial sectors.

Overall loan volume of $1.2 billion was up about 9 percent from a year ago, he said. Deposits of the firm's 12 subsidiary banks and affiliates rose 5 percent to $1.9 billion, while assets increased 7 percent to $2.25 billion.

Potomac Electric Power Co. a Washington-based electric utility that serves the city and populous Maryland suburbs reported second-quarter profits of $13.8 million (26 cents compared with $11.7 million (23 cents) a year ago. Revenues rose to $166 million from $147 million.

In the first six months however profits continued at a depressed level of $26.3 million (50 cents compared with $26.7 million (55 cents) in the 1978 period. Revenues rose to $340 million from $309 million.

On a 12-month basis of comparison Pepco earned $1.65 a share in the period ended June 30 compared with $1.73 in the prior 12 months.

Directors voted yesterday to approve a quarterly dividend of 33 1/2 cents a share payable Sept. 28 to owners of record Aug. 30. Regular payouts on preferred and preference stocks will be paid Sept. 1 to owners of record Aug. 9.