Two District banks and investor groups yesterday launched separate bids to buy a major interest in a third institution, Security National Bank, whose directors quickly met and voted for a merger with a smaller bank in favor of acquisition by a larger one.

Board members of Security, which had assets of $139 million at midyear, voted to approve a combination with Washington Bank N.A. -- whose owner, veteran financier Leo M. Bernstein, would become board chairman and the largest stockholder of Security, the surviving bank.

Rejected by the board, as of last night, was an offer by the holding company of Madison National Bank James Madison Ltd. proposed to buy 44 percent of Security's 400,000 outstanding shares of $60 each and to exchange one share of Madision common stock for each of the remaining shares of Security. Madison, whose stock was quoted at $55 a share yesterday, would be the surviving institution under the takeover that was rejected.

Security Chairman Robert Koontz said yesterday his board concluded that a merger with Madison under terms publicly announced yesterday but proposed in earlier, private discussions, "would not be in the best interests of Security or its shareholders." He said Security and Madison officials had been talking a combination for several months and that the formal offer yesterday "was on substantially the same terms as those previously considered unacceptable" by a special board committee, apparently because book value of the surviving bank would be less than that of Security today, after deducting costs of the takeover.

Stock of Security Bank, with a book value of about $37 each, has been quoted in the over-the-counter market this week at $56 a share, up sharply from $35 earlier this year but below the $72-per-share that Washington restaurant owner Ulysses (Blackie) Auger reportedly paid earlier this year for about 5 percent of Security stock. The earlier stock transaction was seen as the start of a possible bidding war for Security, whose eight D.C. offices and robust profitability are major attractions in an era when interstate banking is considered a strong prospect.

Koontz and Bernstein said last night that under an agreement in principle approved by their boards, stock of Washington Bank will be converted into stock of the surviving bank on the basis of relative book values on June 30. They estimated that each share of Security will be equal to 9.736 shares of Washington Bank for the purposes of a merger, which must be approved by stockholders and federal regulators.

Washington Bank, acquired last year by Bernstein in a takeover approved by federal regulators, formerly was a troubled bank called Diplomat National. With assets of $20.7 million on June 30, Washington Bank has one office on K Street NW. Berstein earlier was vice chairman of National Savings & Trust.

If the merger takes place, Koontz would become chairman of the executive committee and continue as chief executive of Security while Schaefer would continue as president and chief administrative officer.