Joe L. Allbritton, who took control of Riggs National Bank in 1981, completed his sweep of the company's top management yesterday when Daniel J. Callahan III resigned as chairman of the bank's parent company.

Callahan, 50, was ousted as president of Riggs bank by Allbritton last January when the Texas financier took full executive and operating control of the venerable $3.7 billion institution. He kept the title of president of Riggs National Corp. But the job had virtually no power since the parent company's only asset is Washington's largest bank.

Thomas W. Wren, president of Allbritton's University Bancshares Inc. in Houston and vice chairman of Riggs National Corp., will succeed Callahan, who also resigned as a director of the bank and the parent company.

Allbritton, who spent $70 million to buy 40 percent of Riggs in 1981, took full management control of the institution after the bank's earnings began to decline and its problem loans--primarily real estate and international--began to grow sharply. Its list of problem assets, which was $64.3 million at the end of 1981, was trimmed to $37.6 million by the end of last year, Allbritton reported recently.