Senator Elizabeth Warrren told Mr Stumpf he should step down as his bank had "squeezed" its employees "so they would cheat customers".
Bank workers had opened more than two million deposit and credit card accounts without customers' permission.
Mr Stumpf said he was "deeply sorry" for that and failing to act quickly.
The bank was fined $185m (Â£142m) earlier this month and accused of "widespread illegal practice" by the regulator.
Wells Fargo fired more than 5,000 staff in response to the scandal.
"I am deeply sorry we failed to fulfil our responsibility," said Mr Stumpf, before a hearing of the Senate banking committee.
"There is no question with some of our customers we violated trust," he added.
"We never directed nor wanted our team members to provide products and services to our customers that they didn't want.
"That said, I accept full responsibility for all unethical sales practices," he said.
But Senator Warren, who has long been a critic of the US banking industry, was unmoved by his apology.
"You squeezed your employees to the breaking point so they would cheat customers,'' she said.
"You should resign. You should give back the money you took while the scam was going on," she added.
Mr Stumpf has so far ignored calls for him to step down from his post in the wake of the scandal.
"We recognise now that we should have done more sooner to eliminate unethical conduct or incentives that may have unintentionally encouraged that conduct," he said.
Wells Fargo said it would be contacting every deposit customer across the country to see if their accounts were properly authorised.
It will also contact hundreds of thousands of customers with open credit cards to see if they want or need those cards.
In the future, confirmation emails will be sent to customers within one hour of the opening of a new deposit account.
The fine imposed on the bank by the US Consumer Financial Protection Bureau was the largest ever imposed by the regulator.
During fierce criticism from a panel of US senators, Wells Fargo chief executive John Stumpf was told to resign over a bogus accounts scandal.