Riggs National Corp., making its first move into the U.S. retail banking market outside the Washington area, yesterday announced plans to buy Sunset Financial Corp. of Miami for $6.35 million in cash.

The purchase, approved by the Riggs board, was the third banking acquisition Riggs has made in 18 months. But Riggs officials suggested yesterday that the purchase of Sunset is likely to be the Washington bank's most significant, serving as the springboard for a major expansion into Florida.

"This gives us a beachhead from which to expand in one of the fastest-growing states in the eastern United States," said David Palombi, a Riggs vice president and director of communications. "The way we look at it, this could be a major market for us in the future."

The Riggs offer will be presented to Sunset's board for approval Nov. 12. The offer is also subject to approval by federal and state regulatory officials. But Palombi said Riggs did not expect any difficulties that would upset the deal.

Sunset Financial is the holding company for Sunset Commercial Bank, a relatively small state-chartered bank with four branches in Miami and Dade County. Founded in 1979, it has about $75 million in deposits and $84 million in assets. By comparison, Riggs, the Washington area's largest bank, has about $4.6 billion in deposits and $6.07 billion in assets.

Riggs was attracted to Sunset in part because of the relatively large number of its depositors who now live in Florida, mostly Washington area residents who have bought retirement homes there, according to Palombi.

Partly to accommodate these customers, Riggs in 1981 set up an international banking division in Miami. That office is located on the same block as Sunset, another reason Riggs officials were interested in buying it, Palombi said.

Sunset will be merged with a newly formed subsidiary of Riggs, and the surviving company will operate under the name Riggs National Corp. of Florida. Riggs also will consider converting Sunset into a national bank and operating it under the name Riggs National Bank of Florida.