The company is reducing the cost of EpiPens to some consumers through the use of a savings card that will cover up to $300 for the EpiPen 2-Pak. Eligible patients who were previously paying the full price for the EpiPen will have their out-of-pocket cost cut by 50 percent. Mylan also is doubling the eligibility for its patient assistance program.
But Bresch said to do that, she had to go "around the system," and that drug list prices were only part of the problem causing a health-care crisis in the U.S.
"Congress and the leaders of this country need to quit putting their toe in this topic and really fix this — we have an outdated system," Bresch said. "The patient is paying twice."
She also called on patients to "get engaged" with their health care.
"People don't understand their coverage — and how could they? It's complicated," she said. "This isn't a Mylan issue. This is a health-care issue."
Bresch is the daughter of Sen. Joe Manchin, D.-W.Va.
On Thursday, Manchin said, "I am aware of the questions my colleagues and many parents are asking and frankly I share their concerns about the skyrocketing prices of prescription drugs."
"Today I heard Mylan's initial response, and I am sure Mylan will have a more comprehensive and formal response to those questions," Manchin said. "I look forward to reviewing their response in detail and working with my colleagues and all interested parties to lower the price of prescription drugs and to continue to improve our health care system."
CNBC also reached out to Sen. Amy Klobuchar, D.-Minn., for comment. Klobuchar has asked the Federal Trade Commission to investigate price increases at Mylan.
Rep. Elijah Cummings, D-Md., the ranking member on the House Committee on Oversight and Government Reform, issued a statement Thursday that called Mylan's new discount "meager" and noted it came only after "widespread bipartisan criticism."
It is "the same tactic used by drug companies across the industry to distract from their exorbitant price increases, as our investigation has shown repeatedly," Cummings said. "Nobody is buying this PR move anymore. Mylan should not offer after-the-fact discounts only for a select few — it should reverse its massive price increases across the board immediately."
Cummings said he has requested that the oversight committee hold a hearing in September to determine exactly how and why this company drastically raised EpiPen's prices.
Grassley will be on CNBC to discuss the issue at 2:30 p.m. ET.
Watch the full interview with Mylan CEO Heather Bresch here.