WASHINGTON—Regulators ordered five big U.S. banks to make significant revisions to their so-called living wills by Oct. 1 or face potential regulatory sanctions, a stern warning that will fuel criticism the firms are “too big to fail.”

J.P. Morgan Chase & Co., Wells Fargo & Co., Bank of America Corp., Bank of New York Mellon Corp., and State Street Corp. were told by the Federal Reserve and the Federal Deposit Insurance Corp. that the regulators felt their plans for a possible bankruptcy don’t meet the legal standard...