Clients were able to use accounts "held with ING Netherlands for criminal activities for many years, virtually undisturbed," the prosecutors added.
In a statement, ING said: "Koos Timmermans will step down from his position as the chief financial officer and member of the executive board of ING group and will leave the company."
The Amsterdam-based group added: "His resignation follows the announcement of the settlement regarding the shortcomings in the execution of customer due diligence policies to prevent financial economic crime at ING Netherlands." The affair threatens to seriously damage ING's image and has prompted calls for the resignation of its top management.
The influential financial daily Het Financieele Dagblad reported on Monday that Amsterdam was considering dropping ING as its in-house banker over the issue.
"We deeply regret the shortcomings found and take this matter very seriously," said Hans Wijers, who chairs ING's supervisory board.
"Given the seriousness of the matter and the many reactions among stakeholders since the announcement... we came to the conclusion it is appropriate that responsibility is taken at executive board level," Wijers said.