American Security Bank has won federal approval to expand dramatically its international banking operations and will open a new Miami institution next month in an effort to garner a larger share of the Latin American trade.

On the heals of that move by American Security, Riggs National Bank is planning to follow suit by seeking Federal Reserve Board approval to open a similar Miami office. The Florida-based businesses by Washington's two largest banks will offer virtually all corporate banking services for international customers.

"Our concept is that we've embarked on a substantial program that will allow us to compete for international business from American multinationals and nationals," said Louis J. Mulkern, vice chairman of American Security.

Under a law commonly known as the Edge Act, as amended in 1978, U.S. banks may open separate out-of-state offices designed to handle international business. Generally, banks are prohibited from doing normal bank business across state lines.

The Federal Reserve, which must approve the Edge Act expansions, has handled 15 applications to date. But when American Security won Fed approval for the move late last month, that decision marked the first time a Washington bank had received government approval to effectively expand its operations outside the District's borders.

Separately, American Security is planning to open a domestic loan production office in Miami and a separate trust advisory business there -- designed, in part, to handle investments for Washingtonians who move to Florida upon retirement.

In addition, American Security plans to extend its Florida operations by applying for permission to open a limited purpose trust company in Florida. b

Already the bank has loan production offices in Rockville, Tysons Corner, New Orleans, Richmond, Cincinnati and Birmingham, Ala. -- the only such business lending facilites out side the city by a D.C.-based bank.

American Security plans to offer services through its Miami office that are directed primarily to Latin America, the source of about a third of the banks's international business.

Those services include loans and other financial work to support exports and imports, negotiate credit, purchase foreign currency, take deposits from foreign corporations and individuals, distribute economic information from abroad and perform services for corresponding foreign banks. Branches of the Miami operation later could be opened in other U.S. cities. b

About 20 percent of American Security's total loan protfolio is managed by its international division and the bank plans further expansions in that end of its business. In fact, American Security plans to expand its international division from 20 employes to 34 during 1980, according to its Edge Act application to the Fed.

In addition, both American Security and Riggs do business with a number of Latin American embassies and the Miami offices would make those transactions easier.Some of the embassies are required to maintain deposits in Florida, American Security said in its application.

"Establishment of the proposed operation in Miami, Fla., will promote the desired global diversity of American Security with emphasis on Latin America," the bank said.

James D. M. McComas, Riggs' executive vice president and head of international business, revealed yesterday that Riggs will ask the Fed for permission to open a Miami outlet. "We are carefully reviewing other potential sites," McComas added.

Riggs is waiting for U.S. and Bank of England approval of its application to open a full branch in London and expects to get that designation within a couple of months, McComas said. Riggs has a representative office there now and a full branch would be the first in Europe by a D.C. bank.

Dale Jernberg, president of the National Bank of Washington, said NBW officials are studying the Edge Act options before them. Jernberg said that he is not certain whether the capital needed to start such a program -- $2 million under federal guidelines -- could best be spend in that fashion.

Francis G. Addison III, chairman of Union First National Bank, said his institution is "not planning to follow that route."