The federal government announced that all of Silicon Valley Bank's clients would have access to their money starting Monday morning.

The news came after U.S. Treasury Secretary Janet Yellen said earlier on Sunday that the government would not bail out the bank, instead focusing its efforts on concerned depositors.

"Today we are taking decisive actions to protect the U.S. economy by strengthening public confidence in our banking system," the joint representatives of the Treasury, Federal Reserve and Federal Deposit Insurance Corporation said in a statement on Sunday. "This step will ensure that the U.S. banking system continues to perform its vital roles of protecting deposits and providing access to credit to households and businesses."

The statement appears to cover deposits worth more than the $250,000 limit for federal bank insurance.

FDIC representatives said they closed out a second bank, New York-based Signature Bank, on Sunday. Signature Bank will receive a "similar systemic risk exception," and the government agencies promised to bail out depositors, according to the statement.

The Federal Reserve Board will also make additional funds available to eligible depository institutions to ensure that other banks are able to pay their depositors.