The CEO of Silicon Valley Bridge Bank is asking customers to return. But spooked Americans are moving billions out of smaller banks and into Wall Street giants.

• The CEO of Silicon Valley Bridge Bank asked customers to move their money back to the bank.
• US depositors have been moving billions of dollars from smaller to larger banks, per Reuters.

The new CEO of Silicon Valley Bridge Bank is asking customers to help the lender by moving back the money they had withdrawn over the last few days.

"The number one thing you can do to support the future of this institution is to help us rebuild our deposit base, both by leaving deposits with Silicon Valley Bridge Bank and transferring back deposits that left over the last several days," Tim Mayopoulos said in a Tuesday statement.

The bridge bank, which opened on Monday, is a new lender created by the Federal Deposit Insurance Corporation, which took over the deposits of the Silicon Valley Bank.

"If you, your portfolio companies, or your firm moved funds within the past week, please consider moving some of them back as part of a secure deposit diversification strategy," Mayopoulos added.

His statements come just as US depositors are moving billions away from smaller banks after the collapse of Silicon Valley Bank and Signature Bank, New York, Reuters reported Tuesday.

Consumers are now moving these deposits to larger banks, such as Bank of America, Citigroup, and JPMorgan Chase, Reuters reported, citing sources familiar with the matter.

These larger banks have been flooded with requests from customers trying to shift their deposits and are trying to help them set up their accounts quickly, the Financial Times reported Tuesday, citing several people familiar with the matter.

Despite the demand, the larger lenders have been cautious about actively soliciting customers amid jitters in the banking sector, because they are concerned about spurring further fund flows from smaller banks, per Reuters.

Both Silicon Valley Bank and Signature Bank, New York, experienced runs on deposits that led to their closures. In the worst-case scenario, bank runs could leave lenders with too little cash for operations. If the contagion spreads, the financial system could be impacted.

And consumers are moving funds to larger banks despite the US government guaranteeing all deposits at Silicon Valley Bank and Signature Bank, New York, and rolling out a package of emergency measures on Sunday to contain the crisis.

But the hits keep coming for the smaller banks.

On Monday, rating agency Moody's put two regional banks — First Republic and Western Alliance — under review for possible downgrades. First Republic shares tanked 55% to $39.63 apiece on Monday, following the wild weekend in the banking sector. They rebounded to close 27% higher on Tuesday and extended gains by another 8.5% in after-hours trade. Western Alliance closed 43% on Monday and closed 14.4% higher on Tuesday.

Citicorp declined comment to Insider. Bank of America, and JPMorgan did not immediately respond to Insider's requests for comment sent outside regular business hours.