The chairman of the District's largest bank predicted yesterday that if the federal government doesn't take firm measures to curb inflation and rising interest rates, the world economy could dive into a recession.

Vincent C. Burke Jr. made the gloomy prediction at Riggs National Bank's annual stockholders' meeting.

Foreign governments are being forced to follow the lead of the United States and raise interest rates, Burke said. "This is leading to an international interest rate war, which could cause serious economic reversals in all countries," he said.

"With recessions in other countries, our exports would be hurt, which inturn adds to our balance-of-payment woes," he said. "This situation could also lead to a worldwide recession."

Burke predicted that short-term interest rates -- and the prime rate in particular -- will continue to rise, encouraging "anticipating borrowing" by corporations trying to gather money "ahead of any kind of controls."

He said bank officials assume that the Federal Reserve will continue to maintain high interest rates to bring monetary growth and inflation under control.

"If inflation continues, we could expect further Federal Reserve monetary restraint, with further increases in the discount rate or even an increase in bank reserve requirements," Burke said.

Despite the economic forecasts, Burke and Riggs President Daniel J. Callahan painted a rosy picture of Riggs operations in 1979 and in the coming year.

Riggs reported profits of about $21.7 million last year, an 18 1/2 percent increase over 1978 results. Like most banks, Riggs is showing a steep drop in savings deposits, losing $28 million last year, Callahan said. In fact, as of last week, that figure had jumped to $40 million over the past 12 months.

Stockholder gadfly Evelyn Y. Davis asked the bank management several questions, including some about several fees the bank pays.

In response to her questions, Burke said the company paid $941,000 in legal fees last year, donated $248,000 to charities and paid $42,000 for membership in the D.C. Bankers Association and $20,000 for membership in the American Bankers Association.

While Riggs management addressed the stockholders, a local citizens group, the D.C. Bank Campaign picketed outside at the bank's main office on Pennsylvania Ave.

The group's literature criticizes Rigg's lending and foreign investment policies. "We're trying to tell the shareholders what Riggs is doing," said David Neigus, a spokesman for the group.

Specifically, the group charged that Riggs has invested at least $7.5 million in South Africa and has granted loans and lines of credit of at least $73 million to the Chilean government.

Further, the group is complaining that Riggs has granted mortgage money in a disproportionate share to home buyers in affluent neighborhoods of the District.

Callahan denied the charges about local redlining and said that Riggs' credit terms don't reflect neighborhood locations. The charges weren't addressed in depth during a stockholders meeting.

Meanwhile, United National Bank also held its stockholders meeting yesterday, emphasizing the bank's interest in aiding inner city redevelopment.

The bank, now in its 16th year, reported profits of $563,000 last year, up from $103,000 in 1979.