The Federal Reserve's regulation, known as the "total loss absorbing capacity" rule, or TLAC, will require the bank to issue another $60 billion of long-term debt.

Asked in an interview on CNBC whether the $60 billion of total loss absorbing capacity makes the bank safer, Stumpf replied, "Now you're really getting under my neck a little bit, but I don't think that's something that we really needed."

He added, however, that the bank would be able to manage the issuance.

The TLAC requirements, proposed Oct. 30, are aimed at ensuring that some of the biggest and most interconnected banks can better withstand another financial crisis by turning some of their debt, particularly debt issued by their holding companies, into equity without disrupting markets or requiring a government bailout.

The requirement is more difficult for Wells because the bank relies more on deposits, which are less costly than long-term debt, to fund its operations. Securities firms like Goldman Sachs Group Inc and Morgan Stanley, which fund themselves with long-term debt, are not expected to have to issue new debt to comply with the rule.

A Fed spokesman declined to respond to Stumpf's criticism, but pointed to a statement by Fed Chair Janet Yellen the day the rule was proposed. Yellen said the rule "would substantially reduce the risk to taxpayers and the threat to financial stability" from the failure of systemically important firms such as Wells.

(Reporting by Dan Freed in New York; Editing by Dan Wilchins and Dan Grebler)

By Dan Freed