The surprise announcement by Robert Allbritton on Monday comes a few days after he and his family agreed to pay $1 million to a new $9-million fund for victims of former Chilean leader Augusto Pinochet.
Pinochet is said to have hid money in Riggs with the help of bank officials. The Washington bank is paying the remaining $8 million.
Riggs pleaded guilty in January to a criminal felony charge of failing to report suspicious transactions to the authorities and has agreed to pay $41 million in civil and criminal fines to the US government.
Asked whether pressure from federal bank regulators or PNC had figured into his decision to resign, a spokesman for Allbritton from outside Riggs, Sean Kevelighan, replied: "It was his own decision."
Allbritton, 37, assumed control of the bank from his father, Joe Allbritton, several years ago. The Allbritton family, a powerful local dynasty, collectively owns nearly 43% of the bank's stock.
Pittsburgh-based PNC Financial Services Group Inc is buying the parent, Riggs National Corp - stripped of the embassy and international business that got the bank into trouble - for some $643 million in cash and stock.