The U.S. Justice Department's criminal head said banks may need to go beyond filing suspicious activity reports when they encounter a risky customer.

"The vast majority of financial institutions file suspicious activity reports when they suspect that an account is connected to nefarious activity," said assistant attorney general Leslie Caldwell in a Monday speech, according to prepared remarks. "But, in appropriate cases, we encourage those institutions to consider whether to take more action: specifically, to alert law enforcement authorities about the problem."

The remarks indicate that banks may be expected to do more than just file SARs, a responsibility that itself can be expensive and time-consuming.

Some banks already have close relationships with law enforcement, said Kevin Rosenberg, chair of Goldberg Lowenstein & Weatherwax LLP's government investigation and white collar litigation group. Ms. Caldwell's remarks "speak to moving forward in a more collaborative way," said Mr. Rosenberg.

A tip-off from a bank about a suspicious customer could lead law enforcement to seize funds or start an investigation, Ms. Caldwell said.