A Northern Virginia travel agency agreed yesterday to refund immediately more than $250,000 owed to vacationers whose charter flights never left the ground and to pay a $60,000 civil penalty to settle a complaint with the Civil Aeronautics Board.

In a related case, the board's enforcement division asked that a $500,000 civil penalty be levied against First American Bank of Virginia, alleging it had permitted money advanced by European-bound vacationers to be deposited in the travel agency's operating accounts instead of a protected escrow account.

The bank, a subsidiary of First American Bankshares, said in a statement it will "defend itself vigorously against these unique and unfounded allegations." Further, the bank said, "no passengers lost any money from the charter flight operations at issue and full refund checks were issued by the bank" in response to all documented claims.

The complaint against the bank came after the board approved a settlement with Davis Agency Inc., the travel agency.

As part of the settlement, Davis neither admitted nor denied allegations that funds advanced by vacationers were not deposited, as required, in an escrow account at First American.

Between 600 and 800 claims for refunds are involved in the case, according to Douglas M. Steenland, an attorney representing Davis. Most claims of those are from individuals, he said.

CAB regulations require charter operators to protect passengers' funds against default or cancellation of a charter. One of the requirements is that an escrow account be established and that the funds in escrow not be mingled with a tour operator's other funds. Then, if a charter flight is canceled for any reason, refunds are made immediately.

There has been growing concern at the CAB that some travel agents organizing charter flights were mingling escrow and operating funds, and thus found themselves unable to repay the passengers if a flight were canceled.

Last year, CAB Chairman Dan McKinnon ordered a broad investigation of charter escrow account procedures.

"This settlement is an indication of our resolve in these matters," McKinnon said. "We consider violations of our rules protecting charter passengers' funds to be extremely serious."

Under the settlement, the Davis Agency agreed to either pay or to process promptly all refund claims and to transmit the claims for payment to First American.

If refunds were not transmitted to First American by yesterday, the penalty would be increased by $75,000; if a Feb. 10 deadline is not met, an additional $150,000 penalty will be assessed.

As of Wednesday, according to attorney Steenland, First American had paid 507 claims totaling more than $172,000.

According to the CAB order. Davis offered numerous charter flights from several U.S. cities to various European destinations during the spring and summer of 1982.

Until the middle of June, the CAB said, passengers' funds were not deposited in an escrow account. Further, Davis sold tickets until Sept. 24, even though its required security bond agreement for the charter flights had been discontinued Aug. 11.

The CAB enforcement division said that First American certified to the CAB in 1981 that it would maintain an escrow account for the Davis Agency and that funds collected by Davis between November 1981 and Aug. 11, 1982, should have been placed in that escrow account. Instead, charter funds were deposited in other, nonescrow accounts, the complaint alleges.

"At least by late April 1982, if not before," the complaint said, "First American Bank knew or should have known that such deposits were in fact funds received by the charter operator from charter participants...."

First American, in its statement, said that it "is confident that the evidence will establish conclusively that the bank has conducted itself in accordance with safe and traditional industry practices which are fully consistent with both the CAB's regulations as well as the bank's duties as a depository bank to charter flight customers."