Executives of Financial General Bankshares Inc. signed a preliminary agreement yesterday to sell Washington's third-largest banking operation to a group of Middle Eastern investors for more than $160 million.

The agreement ultimately would transfer control of the First American banks in Washington, Maryland and Virginia to owners in Saudi Arabia, Kuwait and Abu Dhabi.

In the pact, Financial General agrees to drop its opposition to the two-year effort by the Middle Easterners to buy the bank and to help them secure the approval of state and federal regulators for the purchase.

Technically the papers signed yesterday only set the procedure for making an offer for the bank.

The next step will be to write a final agreement. Then former senator Stuart Symington will be named to the Financial General board as the representative of the new investors.

Yesterday's agreement was signed by Symington and by B.F. Saul II, FGB's chairman and largest stockholder, and a Washington real estate executive.

Symington is chairman of a Netherlands Antilles company that already owns almost 20 percent of Financial General. That company is owned by Sheikh Kamal Adham, former director of Saudi Arabia's central intelligence agency; Faisal Saud al Fulaij, a businessman from Kuwait; and Abdullah Darwaish, manager of the financial affairs of the royal family of Abu Dhabi.

In the agreement signed yesterday, Adham and his associates promise to make an offer to buy all the stock they don't own already for at least $28.50 a share. "The company deems the price to be adequate," the agreement notes.

Until the agreement appeared close, the shares were selling on the American Stock Exchange for about $16; recently they climbed to $23.

The preliminary agreement was signed after a stockholder referendum last month in which 46 percent of Financial General's shareholders indicated they wanted the company to stop fighting the Middle Eastern takeover.

The offer to buy the stock cannot be made until it has been approved by all the states in which Financial General owns banks and by federal regulators. Until now, that approval has been blocked by the refusal of Financial General to cooperate with Adham's group.

Federal banking authorities say there never before has been an unfriendly takeover of an American bank by a foreign buyer. Any fight for control of a bank is unusual, and the Financial General dispute has been the longest-running takeover battle in the business.

It started in December 1977 when Adham's group began buying shares of Financial General with the help of Bert Lance, who had resigned recently as President Carter's budget director.

Lance bought First National Bank of Georgia from Financial General in 1975, then, after leaving the White House, sold it to Saudi financier Gaith Pharoan. When friends of Pharoan were looking for another American bank to invest in, Lance suggested the Financial General chain.

Lance dropped out of the deal after the group was cited by the Securities and Exchange Commission for failing to report the stock purchases.

Financial General is one of a handful of banking companies that operate in more than one state. The chain was organized before the federal government outlawed multistate banking.

Besides the First American banks in the Disctrict, Maryland and Virginia, the group includes Shenandoah Valley National Bank of Winchester, Valley National Bank of Harrisonburg, Peoples National Bank of Leesburg, Round Hill National Bank and Lexington National Bank in Virginia and Eastern Shore National Bank of Pocomoke, Md., plus banks in Kentucky and New York.

In all, the 13 Financial General banks have 143 offices and assets of $2.2 billion.

In the pact, Adham's group promises not to interfere with the management of the individual banks, now run largely by people in the local communities.

The agreement gives control of the stock owned by Adham, al Fulaij and Darwaish to symington for five years. If symington retires, control of the stock shifts to Clark Clifford, Adham's lawyer.

It could take as long as 18 months to complete the transaction, and the deal provides for Financial General shareholders to profit if the value of the bank goes up before the offer is made.

The escalator clause guarantees shareholders 158.333 percent of the book value of their stock, currently $18.55. If the value of the shares keeps increasing at its present rate, they could be worth $20 by the time the deal is completed, and shareholders then would get about $31 a share.

At $28.50, Adham's group will pay $142 million for the roughly 5 million shares outstanding. They paid between $13 and $15 for the 1.2 million shares they already own and have $16 million or more invested already.