The bank's shares fell as much as 25% to hit a record low in European trading after the remark by the chairman of Saudi National Bank.
Founder of the eponymous discount brokerage has seen his wealth drop more this year than any other US billionaire.
The firm says it has sufficient liquidity to handle any volatility and that more than 80% of deposits are insured by the FDIC.
Shares of regional lenders started the week by selling off, with First Republic down 67%, after Friday's collapse of SVB Financial and Signature Bank's seizure by regulators over the weekend.
In a move to shore up confidence in the banking system, the Fed program will provide banks with one-year loans under easier terms than usual.
The FDIC aims to find buyers for the bank's units to enable it to return as much of clients' money as possible.
The bank's customer base of tech startups had become worried and yanked deposits.
While both lenders had unusually fickle bases of depositors, all banks are facing a challenge as rising rates leave them laden with low-interest bonds.
Federal Reserve Chair Jerome Powell warned of a return to bigger interest-rate hikes to cool inflation and the economy.
The proposal, which has little chance of passing Congress, would also raise the top tax rate for Americans making $400,000, to 39.6% from 37%, reversing one of Trump's tax cuts.
