Many of the regional banks have also said that their deposit base has stabilized.
"The regional banks have come under pressure because they are less equipped to handle a withdrawal of deposits the way the big banks are," said Mark Chandler, chief market strategist at Bannockburn Global Forex in New York.
In a move of solidarity, most of the major banks agreed on Thursday to deposit $30 billion in First Republic.
At least four U.S. lawmakers said on Sunday they would consider whether a higher federal insurance limit on bank deposits than the current $250,000 threshold was needed to inspire more confidence in the system.
Buffett has yet to prop up any of the regional banks.