Riggs National Bank, Washington's largest, yesterday announced that it plans to open offices in Baltimore and Houston within the next few weeks.

The new offices will be the first domestic expansion out of the Washington area for the $4 billion institution, which has overseas facilities in London and the Carribbean.

The new offices will not be branches. For the most part banks are prohibited from setting up branches in any other state than the one in which they are chartered.

Like the loan production offices opened several years ago by American Security Bank, the Riggs offices will make and service loans to corporate customers.

Riggs chairman Joe L. Allbritton, who has been a Houston banker for more than 25 years, said the Houston office will enable Riggs to tap both his experience as well as that of other top Riggs officials who know Texas banking and business well. The Baltimore office is a "logical" extension of the bank's regional lending, he said.

Allbritton still owns two banks in Houston although they are not connected to Riggs. Frank L. Langhammer, who was recently named Riggs senior vice president in charge of domestic commercial and corporate lending, previously headed Chemical Bank's Houston operations. Riggs vice chairman Thomas Wren has been a long-time Houston associate of Allbritton's.

Allbritton's attempt to sell University and another Houston bank ended unsuccessfully earlier this week.