Joe L. Allbritton consolidated his control over Riggs National Bank yesterday by ousting Vincent C. Burke as chief executive and taking over the job himself.

Burke will retain his title as chairman of Washington's biggest bank, but without the authority of the chief executive the post is little more than ceremonial. Burke could not be reached for comment last night.

Last year, Allbritton won a bruising takeover battle, bought control of the bank for $70 million and named himself chairman of a newly formed holding company, Riggs National Corp., which owns the $3.6 billion Riggs Bank.

Most observers expected Allbritton to move aside Burke, who unsuccessfully fought Allbritton's move to take control of Riggs. "What surprised me is that it took him [Allbritton] so long," said one informed source. Although Burke kept the title of chief executive for nearly a year and a half, Allbritton has been making major decisions at the bank, sources close to Riggs said.

Allbritton, a Texas financier who owns WJLA-TV (Channel 7) and once owned the defunct Washington Star, holds about 40 percent of the bank holding company's stock.

Sources in the financial community said they expect Riggs soon will move aggressively to try to garner a bigger piece of Washington's banking business.

If the Congress authorizes interstate banking, Riggs will become an attractive takeover target for a major New York, Chicago or California bank that wants a presence in the nation's capital.

Riggs, with assets of $3.6 billion, has seen its earnings decline as its list of problem loans grows. The list of Riggs' so-called nonperforming assets -- essentially past-due loans, loans on which the terms have been renegotiated and real estate that has been foreclosed -- grew 22 percent during the first six months of the year to $78.7 million.

These problem loans were 4.6 percent of Riggs' total loans as of June 30. In 1981, problem loans at the bank grew from less than $20 million to $64.3 million. Although the worldwide recession and high interest rates have caused problems for many banks, Riggs has a heavier proportion of nonperforming assets than most banks.

When it reported its second-quarter profits, which were down 2.8 percent from the year before, the bank cited problems in the real estate industry in Washington. A sizable portion of its problem loans are to foreign countries as the result of an aggressive move in recent years into international lending.

After Allbritton assumed control of Riggs last year, he moved slowly in making changes. Burke remained as chairman and chief executive of the bank, as well as chairman of the executive committee of the parent company. Allbritton became chairman of the holding company and chairman of the executive committee of the subsidiary bank. Burke will continue to chair the executive committee of Riggs National Corp.

A statement released yesterday afternoon by Riggs quoted Burke as saying the bank's board of directors named Allbritton chief executive "in order to strengthen management at the bank level. Such action will enable Mr. Allbritton to take a more active role in the day-to-day operation of the bank by working more closely with present management to ensure that Riggs positions itself to effectively and productively operate in today's banking environment, as well as take advantage of the growth opportunities afforded the bank."