The Financial Services Committee also said that it would be investigating "the role of Washington regulators in monitoring and investigating" Wells Fargo's alleged misconduct.
Wells Fargo issued a statement, saying, "We welcome the opportunity to provide the Committee with information on this matter and to discuss steps we have taken to affirm our commitment to customers."
Stumpf appeared on CNBC earlier this week, where he said he did not plan to resign. "I think the best thing I can do right now is lead this company," he added.
Separately, the Senate Committee on Banking, Housing and Urban Affairs will be holding a hearing on Tuesday at which Stumpf has been called to testify. A Wells Fargo spokeswoman, Erika Reynoso, said that Stumpf would be attending the Senate hearing.
A letter was sent by Hensarling to James Strother, senior executive vice president and general counsel at the bank, that asked for "all records relating to the questionable sales practices" that the bank had provided to the Office of the Los Angeles City Attorney, the OCC and the CFPB.
Additionally, the letter asked Strother to make four senior executives available for transcribed interviews, including Carrie Tolstedt.
The House committee is also looking into how the CFPB and OCC handled the investigation into the bank.
The committee will be asking for "all records related to the allegations of fraudulent or improper activity by Wells Fargo employees, as well as any documents or communications between the Bureau and OCC employees in the course of their review of the bank's sales practices," it said in the statement announcing the investigation.
The announcement of the House investigation comes a little over a week after the alleged misconduct was outlined by authorities.
When the CFPB, OCC and the Office of the Los Angeles City Attorney slapped the $185 million-dollar fine on the bank, Wells Fargo said in a statement that it takes responsibility "for any instances where customers may have received a product that they did not request."
According to a document provided by the CFPB, an internal Wells Fargo investigation found that more than 1.5 million deposit accounts had been opened "that may not have been authorized," which may have been funded by "transferring funds from consumers' existing accounts without their knowledge or consent." Some 85,000 of those accounts generated fees for the bank worth about $2 million.
Additionally, the document revealed that the bank's own investigation found that "employees submitted applications for 565,443 credit-card accounts that may not have been authorized by using consumers' information without their knowledge or consent." Of those, about 14,000 accounts generated fees worth more than $400,000.
Bank officials told ABC News when the fines were first announced that they believed they had fully refunded affected customers. They said that they had paid out a total of $2.6 million.
Over the period of the alleged misconduct -- between May 2011 and July 2015 -- at least 5,300 bank employees were fired, the bank confirmed to ABC News. However, the bank was quick to point out that this figure only represented about 1 percent of its workforce, and said the terminations "reflect our commitment to monitoring and addressing any inappropriate sales conduct."
The employees were opening the accounts in order to "satisfy sales goals and earn financial rewards under the bank's incentive-compensation program," according to the Office of the Los Angeles City Attorney.
And according to the CFPB, Wells Fargo implemented those goals and rewards because it "sought to distinguish itself in the marketplace as a leader in 'cross-selling' banking products and services to its existing customers."
On Sept. 13, following days of criticism, the bank announced that it would stop imposing sales goals on its employees by Jan. 1, 2017.
Asked by ABC News why the goals wouldn't be ending sooner, a bank official said that there are many details to work out and that the bank would be "thoughtfully working through them over the next several months, in consultation with our team members and an independent consultant before finalizing, while ensuring our team members receive fair compensation through the transition."
This story has been updated to include new statements from Wells Fargo. ABC News' Ben Siegel contributed to this report from Washington.