(Reuters) - U.S. Senate lawmakers excoriated Wells Fargo & Co’s chief on Tuesday for his oversight of the bank as it opened 2 million bogus customer accounts, potentially laying the groundwork for new rules and reviving questions of whether banks are “too big to fail.”

Chief Executive Officer John Stumpf told the Senate Banking Committee on Tuesday that customers who had bogus accounts opened in their name will be made whole and compensated for any damage to their credit rating, but some Democratic senators called for his resignation.

Under fire, Stumpf said he has told his managers to do “whatever it takes” to make customers whole, refunding fees or compensating them for damage to their credit ratings. But he stood behind the former executive who ran the unit that oversaw many of the practices, and at times downplayed the scope of the affair.

In answer to a question, he declined to commit to setting aside mandatory arbitration agreements that prohibit clients from suing Wells Fargo. The Consumer Finance Protection Bureau has proposed a ban on such clauses that prohibit class-action lawsuits.

Earlier this month, the lender agreed to pay $190 million in penalties and customer payouts to settle the case involving the creation of credit, savings and other accounts without customers’ knowledge. About $5 million will directly go to customers, many of whom might have paid a small fee on the unwanted accounts.

The revelations are a severe hit to Wells Fargo’s reputation. During the financial crisis, the bank trumpeted itself as conservative, in contrast to its rivals.

Besides potential criminal charges against the company and its executives, Wells Fargo may face pressure from shareholders to change its practices on executive pay and governance.

The scandal also renewed debate over whether U.S. banks are “too big to fail” and need closer government oversight to prevent a massive collapse.

Lawmakers could use the fraud settlement as a springboard for new rules on executive pay, including clawbacks of compensation, and limits on forced arbitration.

Wells Fargo has said its board will assess whether to cancel or claw back any incentive compensation paid to a now-retired executive at the center of the scandal, Carrie Tolstedt.

Democratic Senators Jeff Merkley of Oregon and Elizabeth Warren of Massachusetts called for Stumpf to resign, with Warren saying Stumpf should give back his salary and be criminally investigated.

“You should resign. You should give back the money you took while this scam was going on, and you should be criminally investigated,” Warren said.

The bank’s board of directors is examining what action it should take against company executives, Stumpf told the committee.

“I accept full responsibility for all unethical sales practices,” Stumpf said, adding later, “I apologize to all of the American people and our customers, and I will make it right.”

Lawmakers said the phony bank accounts might have hurt customer credit ratings, increased the cost of a mortgage or car loan. New credit card applications and consumer borrowing trends can weight on an individual’s credit.

“WHERE WAS MANAGEMENT?”

Wells Fargo has acknowledged bank employees “inappropriately opened” the customer accounts and that about 5,300 employees were fired over five years.

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Former bank employees say they were under intense pressure to add accounts for each customer.

Abuses were found as early as 2011, Stumpf said, but bank executives only realized the scale of the problem early last year.

At that time, Stumpf said, managers came to recognize how a pattern of creating phony accounts could be used to boost unwarranted fees.

“It never dawned on us that there could be a cycle,” the CEO said.

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“It just sort of begs the issue of where was management,” said Senator Sherrod Brown of Ohio, the senior Democrat on the panel.

Brown said employees were caught “forging signatures, and stealing identities, Social Security numbers, and customers’ hard-earned cash, so as to hang on to their low-paying jobs and make money for the high-paying executives at Wells Fargo.”

Thomas Curry, the Comptroller of the Currency, said the agency is considering action against individual Wells Fargo executives who may have violated laws or regulations.

The U.S. Attorney’s Offices in Manhattan and in San Francisco are investigating Wells Fargo, a person familiar with the matter said last week.

While Democratic lawmakers were the most outspoken in their attacks, Republicans also grilled Stumpf.

Louisiana Senator David Vitter pressed the CEO on how customer fraud could persist for years and thousands of employees could be fired before the head of the bank got involved.

“Why isn’t this crystal clear proof that an entity as big as Wells is not only too big to fail but it’s too big to manage and too big to regulate?” Vitter asked.

Stumpf said the widespread abuse was “a problem of focus and not of size.”

Stumpf appeared before the congressional panel with a bandaged right hand. He suffered an injury playing with his grandchildren, according to the bank.

Wells Fargo shares rose 2 percent to $46.94.