Perpetual American Federal Savings and Loan Association has agreed in principle to take over a major Virginia S&L holding company, setting the stage for the first interstate merger of financial institutions in D.C.-area history.

Under an agreement reached yesterday, Perpetual American, the region's largest S&L, would acquire First Financial of Virginia Corp., holding company for McLean-based Washington-Lee Federal Savings and Loan Association, to create an S&L with 41 offices here and assets of $1.9 billion.

Officials of the two institutions emphasized in interviews yesterday that the proposed merger is voluntary and is not being organized by the Federal Home Loan Bank Board, an agency which regulates federally chartered S&Ls and which must approve yesterday's plan before it can proceed.

As proposed, the merger violates federal prohibitions against interstate branching except where there are serious financial problems at one S&L. Interstate mergers are allowed to salvage financially troubled S&Ls only after efforts have been made to bring about intrastate merger.

The bank board proposed last year that interstate branching be considered for metropolitan Washington and similar areas but that was denounced by suburban S&Ls.

"I think the bank board is interested in seeing associations consolidate their strength," said Perpetual American Chairman Thomas J. Owen. With assets of $1.5 billion, Perpetual was one of the few S&Ls in the region to have a profit in the first half of 1981--$1.3 million.

Washington-Lee, while one of the largest S&Ls in Virginia, had a first-half loss of $1.9 million as assets and net worth shrunk in the industry's worst period since World War II.

Washington-Lee Chairman and President Richard S. Lawton insisted yesterday, "I think we can survive as an independent institution, but I and my board think that the interests of our stockholders will be better served by a merger with Perpetual American."

Washington-Lee has adequate reserve funds accumulated in past years to cover operating losses, but they aren't "the kind that they'd like to have or that the bank board would like them to have," said Owen.

"We think the merger of the of the two net worth positions will be attractive enough to the bank board so they will find it permissible in their policies to permit the merger," he added. Washington-Lee had total net worth of $9.5 million on June 30 while Perpetual's net worth was $120 million.

Under the agreement reached yesterday, First Financial's stockholders would receive Perpetual American's 5.25 percent savings accounts in an amount equal to the book value of First Financial at the end of the month preceding the transaction, plus 70 percent of the holding company's unearned loan discounts. The minimum value of the transaction would be $16 a share to stockholders of FFV.

Completion of the transaction is subject to a definitive agreement. The merger would give Perpetual American a network of 17 branches in the District, 20 in Northern Virginia and 4 in suburban Maryland (opened before policy blocked further interstate offices). Perpetual would become the only bank or savings institution here with full-service offices in the three jurisdictions.

Perpetual acquired American Federal Savings and Loan Association of the District last year.