National Bank of Washington shareholders yesterday approved the creation of a bank holding company whose primary asset will be the District of Columbia's third largest bank.

Chairman Luther Hodges Jr. said the bank, with assets of $1.1 billion, had to form a holding company--a corporation whose chief function is to own other corporations--in order to give NBW the ability to expand beyond banking.

For example, Hodges said, the bank holding company--which will be called Washington Bancorporation--could buy a savings and loan association, and under certain circumstances, buy one located in Maryland or Virginia to be ready if federal laws are changed to permit banks to operate in more than one state.

But Hodges, in a speech to shareholders at the bank's annual meeting yesterday, said the company will not be able to expand its operations unless it is able to raise new capital. He said the bank's newly elected board of directors will form a capital planning committee to explore ways of raising the needed capital.

Last year, the bank, which wants to raise an additional $20 million in capital, hired the investment banking firm Warburg Paribas to devise a plan and find potential investors.

So far, bank sources said, there has been little progress.

About 76 percent of NBW's stock is owned by the United Mine Workers of America union, which will become the 76 percent owner of Washington Bancorporation. Shareholders will receive a share of the holding company's stock in exchange for each share of the bank they now own.

Hodges told shareholders that while the bank's performance is not yet completely acceptable, it has been improving steadily since 1980. That year he was named chairman following an insider lending scandal at the bank.