“If they’re too big to fail, they’re too big,” he said in an October speech.

He added: “In 1911, we broke up Standard Oil. So what happened? The individual parts became more valuable than the whole. Maybe that’s what we need.”

In January, the White House embraced a proposal by Mr. Volcker that would ban banks that take customer deposits from running their own proprietary trading operations, or making market bets with their own money. It would also limit the share of all financial liabilities that any one institution can hold — besides deposits — but it would be up to regulators to set the limit.

A federal law enacted in 1994 already addresses size by restricting any bank from holding more than 10 percent of the nation’s deposits, although several of the largest banks have been granted waivers from that requirement or used loopholes to evade its intent.

The Volcker proposal resembled an amendment by Representative Paul E. Kanjorski, Democrat of Pennsylvania, that would let regulators dismantle financial companies so large, interconnected or risky that their failure would jeopardize the entire system. The amendment was part of a regulatory overhaul that the House adopted in December, largely along party lines, and is also in the Senate version in a modified form.

At a hearing on Tuesday about the bankruptcy of Lehman Brothers, which caused credit markets to seize up in September 2008, the Fed chairman, Ben S. Bernanke, reiterated that his preference was to limit the risky behavior of banks rather than break them up.

“Through capital, through restrictions in activities, through liquidity requirements, through executive compensation, through a whole variety of mechanisms, it’s important that we limit excessive risk-taking, particularly when the losses are effectively borne by the taxpayer,” Mr. Bernanke said.

But when Mr. Kanjorski pressed him on whether regulators should be allowed to break up big banks, he replied, “It’s something that would be, on the whole, constructive.”