International Bank of Washington has agreed to sell its 22 per cent interest in Financial General Bankshares, Inc., to a group of investors headed by former Navy Secretary J. William Middendorf II, for about $15 million.

At the same time, IB said a final audit for 1976 has been delayed by recent discovery of "valuation and reporting problems" at an unidentified subsidiary, for which a maximum loss was pinpointed at $10 million.

IB said its management believes the maximum amount will be reduced "significantly" by certain claims and recoveries.

Based on a tentative assessment setting aside $3 million related to the subsidiary's problems, IB said its unaudited 1976 profits were $2.28 million (32 cents a share) compared with $2 million (27 cents) in 1975.

Because of the unexpected accounting problem and the loss IB will suffer on selling its shares in Financial General -- a major Washington area bank owner -- IB's shares fell sharply in trading yesterday.

IB common fell to $4.625 bid from $5.75 and Class A fell to $4.625 from $5.875. About 14,500 shares of both classes traded yesterday. The biggest volume in IB stock this week came Wednesday, when 13,400 shares of common and 1,500 class A were traded. IB common opened 1977 at under $4.50 a share and rose to more than $6 before declining gradually in recent weeks.

The 1975 results of IB were restated to reflect the sale of Financial General stock; profits from continuing operations in 1975 were listed as $326,684 (10 cents) and from discontinued operations as $1.2 million (17 cents).

IB said its sale of Financial General would result in a 1976 loss from discontinued operations of $4.8 million (68 cents). The actual Financial General loss was $5.4 million (76 cents), representing the difference between the sale price to Middendorf and the value of Financial General stock previously listed on IB's books.

The Middendorf group agreed to buy IB's shares in Financial General, a bank holding company, at $12.50 a piece, an arrangement that must be approved by the Federal Reserve Board. The Fed has ordered IB to reduce its ownership of the banking firm and the new agreement includes a provision that it must be consummated by next Sept. 30, or either party may withdraw.

IB said the problems uncovered at its subsidiary probably will require adjustments to results reported for prior years.