Maryland's two largest commercial banks are opening offices in downtown Washington to compete for the city's commerical business -- a step that gives the banks a presence in a market that interstate banking may open up to them.

First National Bank of Maryland, the state's second-largest bank with assets of $2.36 billion, opened a Washington office at 18th and K streets NW last Friday, and Maryland National Bank, Maryland's largest with $4 billion in assets, plans to open their D.C. office at 1110 Vermont Ave. NW in midsummer.

And Riggs National Bank, the Washington area's largest financial institution with $3.2 billion in assets, may invade the Maryland banks' Baltimore territory with an office in that city. Such a move appears to be under consideration by Riggs based on remarks by bank officials, although Chairman Vincent Burke denies it.

Behind the moves appears to be increasing competition and jockeying for position by major regional banks anticipating the shakeout in the industry expected to follow major changes, including anticipated approval in the long run of interstate banking.

What appears to be immediately involved is aggressive attempts to expand commercial accounts.

For Baltimore banks, Washington's allure includes the trade associations and growing service industries that dominate the economic landscape here.

For Washington banks, Baltimore offers the promise of industrial, manufacturing and shipping business.

"Manufacturing and trade are better for banking," said National Bank of Washington President Luther Hodges.

Washington and Maryland banks have been doing commercial business in each other's jurisdictions all along, and Suburban Trust of Maryland has an office in Washington.

Banking laws preclude banks from operating branches outside their home states except for loan procurement offices to develop business or branches dedicated only to international banking.

"We've historically been a factor, albeit a modest one, in the Washington financial community," said Allen S. Lloyd Jr., vice president in charge of the D.C. and Northern Virginia banking group for Maryland National.Lloyd has been in charge of planning Maryland National's Washington office and will head it.

"The Washington market has probably been underrated in terms of what is indigenous to it," he said. "It's not heavy industry or port facilities, but many kinds of businesses -- principally service business -- abound down there."

Among other steps preparing for opening its Washington office, Maryland National has been advertising heavily in this area. Riggs recently advertised in Baltimore papers, a sign that some in the Baltimore advertising and banking communities interpreted as a signal of an entry there. One advertisement featured the skyline of Baltimore. "Shipping through Baltimore? . . . Finance through Washington," the ad said.

Although Riggs Chairman Burke denied that the bank was even considering an office in Baltimore, Senior Vice President and Cashier Melvin Chrisman said, "There's alot of feeling that the Baltimore-Washington area ought to be more homogenized. There's a good deal of talk about it. There are a lot of pros and cons."