“The goal to end too big to fail and protect the American taxpayer by ending bailouts remains just that: only a goal,” Thomas M. Hoenig, the vice chairman of the F.D.I.C., said in a statement.

The regulators were responding to the so-called living wills that banks must submit to regulators on a regular basis to explain how the banks plan to enter bankruptcy in an orderly fashion in case of a crisis. The living wills are a requirement of the 2010 Dodd-Frank financial overhaul, intended to help make large financial institutions less of a threat to the wider economy.

The Fed and the F.D.I.C., which jointly oversee the largest banks, agreed that the plans put forward by five of the big banks, JPMorgan, Bank of America, Wells Fargo, State Street and Bank of New York Mellon, were “not credible or would not facilitate an orderly resolution under the U.S. Bankruptcy Code.”

Only one of the biggest banks, Citigroup, was given a passing grade by both agencies, though it too was told that its plans needed improvements. Goldman Sachs and Morgan Stanley received passing grades from only one of the two agencies.

Barney Frank, the former Massachusetts congressman who was one of the architects of the Dodd-Frank law, said on Wednesday that the rejection of the living wills indicated that the regulators believed they still have more to do to tackle the too-big-to-fail issue. But he added that the regulators were showing resolve.

“It sends a message,” Mr. Frank said in an interview. “It signals that they are serious.”

In recent weeks, Mr. Frank has criticized the financial overhaul proposals by Mr. Sanders. Mr. Frank contends that some of the plans to break up the banks are simplistic because they take a one-size-fits-all approach. In contrast, he said, measures like the living wills allow regulators to press for banks to shrink, based on specific conditions at those firms.