Jorge E. Carnicero and two of his nominees were elected to the board of Riggs National Bank yesterday, completing what Riggs Chairman Vincent C. Burke Jr. described as "an accommodation" between the bank's management and its biggest single stockholder.

Carnicero, who had been on the Riggs board, was joined by his daughter, Jacqueline C. Duchange, and Merlon F. Richards exxecutive vice president of Dynalectron Corp., the McLean electrical contracting firm headed by Carnicero.

Carnicero and companies he controls own more than 265,000 shares of Riggs stock recent reports to the Comptroller of the Currency show. Since January 1977, Carnicero has purchased more than 150,000 shares of Riggs, worth more than $6 million at current prices.

Burke told shareholders that Carnicero's holdings are great enough to allow him to elect three of Riggs' 25 board members under the cumulative voting required by federal law for bank boards. Cumulative voting gives a shareholder one vote for each share of stock for each open seat, and allows all the votes to be concentrated on a few nominees, assuring their election.

"It is not a question of the bank giving Mr. Carnicero three directors, it is a question of someone exercising their rights," Burke told a shareholder who questioned the action.

Rather than face a contested election, he added, the bank's management decided "it was better to reach an accommodation with Mr. Carnicero."

Burke said Carnicero assured bank officials he has no interest in using his investement to gain control of the bank, and Carnicero repeated that pledge in an interview after the meeting.

"I've said it before; this is an investment, an excellent investment," Carnicero said. "The bank has an excellent management team. This is the finest city in the country. It is an excellent investment."

Burke in turn praised Carnicero's board member daughter as "a very bright, alert person" and called Richards "a prominent businessman." Duchange, who studied at Harvard's Graduate School of Business, is the second woman on Riggs' boartd, serving with Margaret Truman Daniel, a member since 1977.

Carnicero spoke briefly during the annual shareholders meeting of the bank, affter shareholder Evelyn Y. Davis asked if he had borrowed money to buy his Riggs stock from a foreign bank.

"It was a very large national bank here in the United States.It was not a foerign bank," said Carnicero.