The company has faced a heated backlash from customers, policymakers and the media after video footage surfaced of one passenger, Mr David Dao, being dragged from a United Airlines flight that officials falsely believes was overbooked.
"The incident has been a humbling learning experience for all of us here at United", he said.
In response to the public outcry over the incident, United has said that it will require its employees to book seats on hour in advance, to avoid similar incidents of passengers being forced to give up their seats after boarding.
He had initially said, in an internal email later leaked to journalists, that Dao had been "disruptive and belligerent" and staff were "left with no choice".
Munoz and other top airline executives apologized again for the fiasco on Tuesday before discussing the airline's latest financial results on a conference call with analysts and reporters.
The airline's first-quarter revenue increased 2.7 percent to $8.4 billion.
"It was a system failure across various areas", Mr Munoz continued.
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Munoz has already stopped at the Chinese consulate in Chicago to try to smooth over the situation, with the company concerned the incident would affect bookings from Chinese customers. Meanwhile, a petition on Change.org calling for Munoz's resignation continues to grow.
Dao's lawyers have taken steps that foreshadow a lawsuit against the airline and the city of Chicago, which operates O'Hare Airport.
The violent incident was caught on another passenger's cell phone video that went viral and sparked widespread outrage at the airline and the security officers who bloodied the doctor.
And some U.S. politicians have called for a total ban on overselling flights.
Munoz declined to comment on any other policy changes coming to United Airlines, according to The Tribune.
Scott Kirby, airline president: It's really too early for us to tell anything about bookings and in particular last week because it was the week before Easter. Dao emigrated to the United States from Vietnam. He said he had conferred with the company's board of directors and expects to remain as the airline's chief executive despite calls for him to resign.
"We are looking at a broad array of issues", Munoz said.
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