"I accept full responsibility for all unethical sales practices," CEO John Stumpf told a congressional panel.
Stumpf said later, "I apologize to all of the American people and our customers and I will make it right."
The bank's board of directors is examining what action it should take against company executives, Stumpf told the Senate Banking Committee.
Earlier this month, the lender agreed to pay $190 million in penalties and customer payouts to settle a case in which bank employees created credit, savings and other accounts without customer knowledge.
Of the $190 million in the settlement, only $5 million will go directly to compensate customers, many of whom might have only paid a small fee on unwanted accounts.
But lawmakers said phony bank accounts might have hurt customer credit ratings, potentially increasing the cost of a mortgage or car loan. New credit card applications and consumer borrowing trends can weight on an individual's credit report.
Thomas Curry, the Comptroller of the Currency, said in prepared testimony that his agency is considering action against individual Wells Fargo executives.
"The OCC may take formal enforcement actions against institution-affiliated parties, including directors, officers, and employees, who violate any law or regulation, engage in unsafe or unsound practices, or breach fiduciary duty," Curry told a hearing of the senate committee.
Sherrod Brown, the senior Democrat on the senate panel, blasted Wells Fargo for exploiting customers and the bank’s slow response to control the abuse.
"I was stunned when I learned about the breadth and duration of this fraud," the Ohio lawmaker said in his opening remarks.
Wells Fargo has acknowledged bank employees abused customers over five years and about 5,000 employees were fired in that time.
Former bank employees have said they were under intense pressure to add accounts for each bank 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, bank executives came to recognize 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.
By early 2015, thousands of bank employees had been fired, the Los Angeles Times newspaper had reported the abuses and prosecutors were investigating.
“It just sort of begs the issue of where was management,” Brown said.
Brown pressed Stumpf to pledge to go back prior to 2009 in his review. Stumpf said he would "take it under advisement."
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."
Democratic presidential candidate Hillary Clinton, in a letter to bank customers released on Tuesday, said Stumpf "owes all of you a clear explanation as to how this happened under his watch."
Clinton, who was criticized during the Democratic primaries for representing Wall Street interests, laid out a plan to address what she called "the culture of misconduct and recklessness" in the banking system.
It included "clawing back" the compensation of individual executives involved in wrongdoing and breaking up big banks that are not managed effectively.
Officials from the campaign of Republican presidential nominee Donald Trump did not immediately reply to requests for comment on the Wells Fargo matter.