Just when it seemed that Riggs National Bank, "the most important bank in the most important city in the world," might be forced to share that distinction with new and bigger competitors, management served notice last week that it will have none of that.

Riggs National Corp., the holding company for Washington's biggest bank, created a flurry of speculation last week with an intriguing three-part announcement: Directors declared a stock split, raised the quarterly cash dividend 10 percent and disclosed plans for a public stock offering.

The coincidence in the timing of Riggs' announcement and the completion of Norfolk's Sovran Financial Corp.'s merger with D.C. National Bank did not go unnoticed. Sovran's acquisition of D.C. National and its earlier merger with Suburban Bancorp of Bethesda underscored Sovran's ranking as the region's biggest bank company, with assets in excess of $13 billion.

Whether coincidental or not, last week's announcement by Riggs diverted some attention from the Sovran-D.C. National merger.

Aside from its obvious importance to investors, Riggs' announcement had a great deal of significance for observers of Riggs and its chairman and principal stockholder, Joe L. Allbritton. Not surprisingly, the announcement rekindled speculation -- about Allbritton's intentions and Riggs' future -- that began with the financial entrepreneur's acquisition of 42 percent of the bank's stock in 1981.

Documents that Riggs filed with the Securities and Exchange Commission just prior to last week's announcement raised the level of speculation to new heights in local banking circles. Proceeds from the stock sale will be used for general corporate purposes and "possibly, acquisitions of banks or nonbanking companies," according a registration statement at the SEC.

Riggs' annual report to shareholders, the timing of which coincided with the release of last week's announcement relating to the company's stock, confirmed plans to which Allbritton had alluded in private.

"We have made it plain that The Riggs is actively and aggressively exploring possibilities that will allow us to expand our banking business to desirable areas beyond the District within our contiguous market region," Allbritton wrote in the annual report to stockholders.

Although Allbritton has declined to be more specific about Riggs' expansion plans, his statement answers at least three questions: Allbritton does not intend, at least not in the near term, to sell his controlling interest in the bank; Riggs won't remain passive as out-of-state competitors take advantage of interstate banking laws to expand and increase market share at Riggs' expense, and Riggs has no interest in expanding its market area beyond Maryland or Virginia.

How Riggs intends to become bigger than Sovran by the end of this decade, as Allbritton has indicated to associates, is still an unanswered question. Riggs would have to merge with at least three regional banks of comparable size (assets of more than $5 billion) to achieve that.

At the moment, Riggs' choices in Virginia have been narrowed considerably by interstate mergers, unless it plans to acquire a small bank in that state. All but one of the leading bank companies in Virginia have either completed or have signed merger agreements, giving them access to D.C. and Maryland. Of the top seven Virginia bank companies, Central Fidelity Banks Inc. of Richmond is the only one that hasn't agreed to an interstate merger. Central Fidelity's management repeatedly has stated its intention to keep its independence.

The situation is decidedly different in Maryland, where only two of the top 10 bank companies -- Suburban and Union Trust Bancorp -- have agreed to interstate mergers. It's possible that a marriage could be arranged between Currently, speculation centers on a possible merger between Riggs and First Maryland Bancorp, Maryland's second largest. Riggs and one of Maryland's top-echelon banking firms, giving the Washington bank a substantial start toward its goal of achieving a size that compares favorably with the assets (roughly $20 billion) of North Carolina's top three banks.

Currently, speculation centers on a possible merger between Riggs and First Maryland Bancorp, Maryland's second largest. Allied Irish Banks Ltd., which owns a controlling interest in First Maryland, had expressed interest in a merger for the Baltimore bank, even though it wants to maintain an investment in it.

First Maryland, the parent of First National Bank of Maryland, terminated negotiations with an unnamed regional bank holding company last summer after announcing that it was holding talks that could lead to a merger.

Reliably informed banking sources believe Allbritton would consider a deal with First Maryland at the right price.

First Maryland's stock closed at $31 a share last week, substantially less than the $69 price of Riggs stock. A stock swap might make the price right for Allbritton. It certainly would double Riggs' assets.