Wells Fargo has begun an “extensive review” of the way it closes customers’ accounts and the fees it charges some customers even after their accounts are supposedly closed, its chief executive, C. Allen Parker, said in a letter to Senator Elizabeth Warren of Massachusetts.

The letter was written on Friday, the same day that Ms. Warren asked regulators, including the Securities and Exchange Commission, to look into the matter.

The practice, which was described in a New York Times article last month, charged customers hundreds or even thousands of dollars in overdraft fees in the weeks after Wells Fargo informed them that it was closing their accounts. The bank ignored complaints that at least two employees raised about the practice.

It is the latest in a series of scandals that have cost Wells Fargo $1.5 billion in penalties and have prompted the Federal Reserve to bar the company from growing until it can fix its culture.