In the panic after Silicon Valley Bank collapsed in early March, some small and medium-size businesses yanked their money from regional banks and deposited it with the biggest ones, seeking the security of their gigantic balance sheets and the government’s implicit backstop of lenders deemed too big to fail.

Regulators, bank executives and industry representatives have been trying desperately to persuade those depositors to stop.

On Tuesday, Treasury Secretary Janet Yellen expressed confidence in the nation’s banks and suggested that the government would step in to protect smaller banks if needed. Shares of many regional banks rallied after her remarks.