D.C. Mayor Marion Barry signed a bill yesterday exempting from taxes income earned by Washington banks from their newly created international banking facilities that make loans to and accept deposits from foreign companies, governments and individuals.

A spokesman for the mayor said the legislation is part of an effort to make Washington a more important international finance center. The District's biggest banks either have or soon will open international banking facilities.

Such banking facilities, which were authorized by the Federal Reserve Board last December, are free of many of the federal regulations that forced U.S. banks to conduct much of their overseas business in branches located abroad.

The new facilities are designed to compete with the so-called Eurocurrency market, a pool of more than $1.6 trillion of currencies that are bought and sold or loaned and deposited in foreign countries. The vast majority of those currencies are dollars on deposit at banks outside the United States.

Since last December, deposits at the nearly 200 international banking facilities set up by American banks have grown from zero to $120 billion. The facilities are not expected to entice U.S. banks to close their branches in major banking centers such as London, but branches in so-called "bank havens" such as the Bahamas or the Cayman Islands are likely to become less important.

Six states--including New York and Illinois, which are home for nearly all the important multinational banks--have exempted the earnings of the international banking facilities from local taxes. Washington joined them yesterday.

The new facilities mean nothing to U.S. companies or individuals. Customers will be confined to foreign corporations, individuals and the foreign subsidiaries of U.S. corporations.

G. Stimson Eveleth, senior vice president and head of the international department at American Security Bank, said Washington's second-biggest bank will concentrate on lending and borrowing money for very short periods, much as it buys and sells money in the domestic money markets.

Although buying money technically is taking a deposit, and selling it is making a loan, bankers differentiate between the short-term banking functions, or what they call trading activities, and the longer-term banking functions, which they call commercial transactions.

International banking facilities are exempt from requirements such as the reserve regulations under which banks have to set aside a certain percentage of every deposit they receive.

So-called Eurodollars, the backbone of the whole Eurocurrency system, technically are dollars owned by nonresidents of the United States. Eurodollars--which neither look nor smell any different than other dollars--are free of U.S. regulations. These Eurodollars now may be deposited at an international banking facility located within the United States and remain free of federal regulations.

The facilities were approved by the Federal Reserve Board in the spring of 1981 after years of lobbying by the major New York banks. The bankers argued they could create jobs and do business in the United States.