Moody's has cut the outlook on U.S. banking system to negative.

"We have changed to negative from stable our outlook on the US banking system to reflect the rapid deterioration in the operating environment following deposit runs at Silicon Valley Bank (SVB), Silvergate Bank, and Signature Bank (SNY) and the failures of SVB and SNY," Moody's said in a report.

In its downgrade of the entire sector, the rating agency noted the extraordinary actions taken to shore up impacted banks. But it said other institutions with unrealized losses or uninsured depositors still could be at risk.

"Banks with substantial unrealized securities losses and with non-retail and uninsured US depositors may still be more sensitive to depositor competition or ultimate flight, with adverse effects on funding, liquidity, earnings and capital," the report said.