Joe L. Allbritton took over as chairman and chief executive officer of Rigg National Corp. yesterday, moving into full operating control of the area's largest banking company.

At the same time, Thomas W. Wren, who oversees Allbrotton's Houston banks, was named vice chairman of the holding company formed to put Riggs in a position to expand in the rapidly shifting financial arena.

The holding company was officially formed May 31 when the Federal Reserve Board granted Riggs permission to do so. The proposal had been advanced by Riggs directors before Allbritton took control of the bank after a struggle with its old leadership.

Vincent C. Burke Jr., chairman of the bank, will serve as chairman of the executive commitee of the holding company, and Daniel J. Callahan III, president of the bank, will be president of the holding company as well.

The organization of the holding company does several things for Riggs. It puts the 145-year-old bank in a position to expand regionally, if and when interstate banking becomes an option, and generally creates a more flexible organizatio;n to deal with the other changes coming in the way financial institutions compete with each other.

It also creates eight vacancies on the board of the $3.5 billion bank, which generally has been a reflection of the old-line, white-male-dominated Washington business community.

Eight former directors of the bank will become directors of the bank holding company. They are developer Oliver T. Carr Jr.; Floyd E. Davis Jr., president of Floyd E. Davis Cos.; Randall H. Hagner, presidnet of Randall H. Hagner & Co.; Harold H. Hall, president of Southern Railway Co.; Mandell J. Ourisman, president of Ourisman Chevrolet; builder Robert H. Smith; Leonard P. Steuart II, president of Steuart Petroleum Co.; and W. Reid Thompson, chairman of the board and president of Pepco.

"This management team and organization will position the corporation to take full advantage of new opportunities provided by the anticipated program of deregulation ad relazation of prohibitions in the financial industry," Allbritton said in a prepared statement. Allbritton was in California at the time of the announcement.

Allbritton effectively gained control of the bank in March after a prolonged struggle with Riggs' management. Ultimately Allbritton and Riggs' directors reached a settlement, and Allbritton acquired 40.1 percent of the bank's stock for approximately $70 million.

Since Allbritton's takeover, there have been no major changes in the bank, but the holding company organization appears to be the first stage in getting the banking firm in position for them.