Bank of Virginia Co. of Richmond yesterday completed an agreement in principle to buy Security National Corp. of Washington for close to $63 million, or $68.50 a share.

The proposed interstate purchase of the District's eighth-largest banking firm would boost Bank of Virginia Co.'s assets by at least $277 million. The bank is already Virginia's fourth-largest bank holding company, with assets of $4.4 billion.

The pact, which is subject to a definitive agreement and regulatory and stockholder approvals, is the third in which a big Virginia bank holding company has agreed to acquire a District banking institution this year.

Bank of Virginia Co.'s purchase of Security National would also give the Richmond firm control of banks in three jurisdictions as part of an interstate banking strategy that has been adopted by its principal competitors in Virginia. Earlier this year, Bank of Virginia Co. signed a definitive agreement to acquire Union Trust Bancorp of Baltimore for about $325 million.

The agreement between Bank of Virginia and Security calls for the purchase of all of the 917,712 of Security's outstanding common shares. In addition, Security agreed in principle to give Bank of Virginia Co. an option to purchase 500,000 authorized, but unissued, shares. The purchase price is 2.73 times book value, or the price of the company's assets as listed on financial statements.

Security National Corp. Chairman Melvin Lenkin, who owns almost 42 percent of the bank's stock, has already announced his intention to vote in favor of the proposed sale.

Upon completion of the transaction, Security would become a wholly owned subsidiary of Bank of Virginia Co., but would continue to do business in the District as Security National Bank.

Frederick Deane Jr., Bank of Virginia Co.'s chairman, would become chairman of Security National Bank and Lenkin would become vice chairman. Thomas J. Schaefer would continue as president and chief executive officer of Security National.

Bank of Virginia operates 133 branches throughout the state. It reported $3.4 billion in deposits at the end of September. Security National, with deposits of $244 million, operates seven branches in the District.

If the merger with Security is approved, Bank of Virginia would be competing in the Washington-Baltimore corridor with Sovran Financial Corp. and United Virginia Bankshares Inc., the two largest bank companies in Virginia.

UVB is expected to complete its acquisition of NS&T Bankshares Inc. later this month. A merger between UVB and Bethesda Bancorp is pending.

In the meantime, at a special meeting yesterday, stockholders of D.C. National Bancorp approved an agreement calling for Sovran to buy the Washington bank company and its subsidiary, D.C. National Bank. Sovran has also signed an agreement to acquire Suburban Bancorp of Bethesda.

In another proposed merger that would give a Virginia banking firm access to a broader market in the Washington area, Dominion Bankshares of Roanoke last month agreed to acquire State National Bank of Maryland in Rockville.