Customers pulled nearly $100 billion from American bank accounts just during the week that Silicon Valley Bank and Signature Bank collapsed.

New Fed data shows that $98.4 billion in deposits was pulled from American banks during the week ending March 15. SVB collapsed on March 10 and Signature Bank was seized by regulators on March 12.

According to the data disclosed, the vast majority of withdrawals came from small banks. Large institutions saw deposits increase by $67 billion as customers switched their money from regional banks to "too big to fail" behemoths.

Seeking to assuage Americans' fears, Federal Reserve Chairman Jerome Powell says deposit outflows "have stabilized over the past week" following the Fed's "powerful actions" to backstop the system.

Treasury Secretary Janet Yellen, Federal Reserve Chairman Jerome Powell, and numerous other high-level officials held a special closed-door meeting of the Financial Stability Oversight Council on Friday, spooking many investors and market watchers.

The only comment made about the meeting was as follows:

"The Council discussed current conditions in the banking sector and noted that while some institutions have come under stress, the U.S. banking system remains sound and resilient. The Council also discussed ongoing efforts at member agencies to monitor financial developments."