Sovran Financial Corp., Virginia's biggest bank company, and Suburban Bancorp, the fourth largest in Maryland, yesterday agreed to merge, creating the biggest financial institution in the Washington region.

The $405 million merger agreement announced yesterday will produce a banking network with more than 300 branches and assets of nearly $12 billion.

In addition, Sovran in July made a tentative agreement to acquire D.C. National Bancorp, the parent of D.C. National Bank, the District's sixth largest with six branches and assets of $348 million. That merger cannot be completed until Mayor Marion Barry decides whether to sign the interstate banking bill passed by the D.C. City Council on Sept. 10. Barry has threatened to veto the measure because it does not open up the District to interstate banking as fast as he would like.

The Sovran-Suburban combination is the fifth proposed interstate bank merger in the Washington-Maryland-Virginia region since last spring when Virginia and Maryland passed laws permitting interstate banking within the region.

United Virginia Bankshares Inc. plans to buy NS&T Bankshares Inc., owner of Washington's NS&T Bank and Bethesda Bancorp., parent of Bank of Bethesda. Bank of Virginia has agreed to merge with Union Trust Bancorp of Baltimore.

At the same time, the big New York banks are pushing hard to get into the Washington area. To get a foothold in Maryland, Chase Manhattan Corp. has agreed to take over Friendship Savings and Loan of Bethesda and Chesapeake Savings and Loan of Baltimore and is negotiating to acquire Merrit Commercial Savings and Loan of Baltimore.

Citicorp, which already has limited banking operations in Maryland, will be free to open 10 branches throughout the state beginning next July as a result of special legislation opening the state to any bank willing to meet certain investment requirements.

To get a jump on that opening, Citicorp also has agreed to acquire First Maryland Savings and Loan of Silver Spring. It also is leading the campaign to speed up interstate banking in the District.

With assets of $8.3 billion, Sovran is already the biggest financial institution in the three jurisdictions, followed by $7.3 billion Maryland National Corp. After completion of the two proposed mergers, Sovran will be more than twice as large as Washington's two biggest banking companies -- Riggs National Corp. and American Security Corp., both of which have assets of about $5 billion.

Sovran was formed in 1983 when First & Merchants Corp. of Richmond, Virginia's fifth-largest bank, and Virginia National Bankshares of Norfolk, the state's second largest, merged to become the largest bank holding company in the Middle Atlantic states.

At the time of the merger, the combined institutions had assets in excess of $7 billion. As of June 30, Sovran, which operates 266 branches throughout Virginia, reported assets totaling $8.7 billion. Suburban reported assets of $3.1 billion and $2.3 billion in deposits at mid-year. It operates 82 branches throughout Maryland.

Yesterday's agreement calls for Suburban shareholders to receive 2.926 shares of Sovran Financial for each share of Suburban common stock. The merger, which is subject to the approval of regulatory authorities and shareholders of both institutions, is expected to be completed in early 1986.

Sovran said it plans to purchase about 3 million of its shares from stockholders on the open market and in private transactions to replace shares that would be used to purchase D.C. National Bancorp.

As part of the agreement, Sovran also received an option to buy 1.8 million shares of unissued Suburban common shares, at $60.50 a share. Sovran Financial stock closed yesterday at 25 3/8, down 3/8, in over-the-counter trading. Suburban moved up 4 1/2 on news of the merger to close at 66.

As a result of the merger, Sovran "will wind up getting a big chunk of the business in this area," predicted Elliott H. Benson, vice president and director of research at Ferris & Co., the Washington stockbroker. Benson said the acquisition would bring together "two highly respected bank companies" with good profits.

"It is consistent with what Sovran has been doing and is consistent with their announced strategy of going after companies that were consistent with their level of profitability -- a 1 percent return on average assets," said Gilbert Keech, vice president at Johnston, Lemon & Co.

Suburban Bank, the principal subsidiary of Suburban Bancorp, will be operated as a separate subsidiary of Sovran and renamed Sovran Bank/Suburban.

Suburban Chairman Robert F. Tardio will remain chairman and chief executive officer of Sovran Bank/Suburban. He will also become a member of Sovran's board of directors and chairman of its executive committee. G. J. Manderfield, Suburban's president, will continue in that capacity and also will join Sovran's board and become a senior vice president of Sovran.

The merger agreement is the culmination of Sovran's initial interstate banking strategy to have a strong presence in three jurisdictions in the middle Atlantic region. The combination of a presence in Maryland and the District, plus Sovran's strategic position in Northern Virginia, will give the Norfolk-based company "one of the strongest market franchises in the country," said C. A. Cutchins III, Sovran Financial's chairman and chief executive officer.

Tardio will retain the titles of chairman and chief executive officer as head of Sovran Bank/Suburban. In addition, he will be nominated to the board of Sovran Financial Corp. and will become chairman of its executive committee. G. J. Manderfield, Suburban's president and chief operating officer, will continue in that capacity at the new subsidiary formed by the merger. Manderfield also will be nominated to Sovran's board and will be named a senior vice president of Sovran Financial Corp.