"I was hired to make United better and we've been doing that and that's what I'll continue to do," Munoz said, when asked about calls for his resignation as leader of the embattled airline on the ABC show "Good Morning America."
Munoz reiterated his regret over the incident Sunday, which sparked widespread outrage and mushroomed into a global public relations disaster after video of passenger David Dao, 69, his face bloodied, being dragged off the plane, went viral.
"Probably the word 'shame' comes to mind," Munoz said, adding that he had not yet spoken to Dao, but his team had tried to reach out to him.
"We've not been able to contact him directly," Munoz said. "I do look forward to a time when I can as much as I'm able to apologize directly to him for what's happened."
Munoz pledged a thorough review of United's procedures and promised that police would not be used in the future to remove passengers.
United also said it would compensate all passengers on Dao's flight.
United shares fell 1.1 percent to end the trading day at $69.93.
'Tone deaf' response
Meanwhile, attorneys for Dao filed papers in Cook County courthouse in Chicago demanding preservation of surveillance video, passenger and crew lists and other evidence, a first step in potential litigation.
"After being duly processed by the ticket agent, checked in by the attendant and seated in his assigned passenger seat, Petitioner was forcibly dragged and removed from the said aircraft by City employees, sustaining personal injury," the filing said.
A spokeswoman for law firm Corboy & Demetrio said Dao remained in the hospital but that a family member is expected to participate in a news conference Thursday in Chicago.
Munoz also faced criticism for his initial response to the crisis in which he appeared to put partial blame for the incident on the passenger, saying he had "defied" authorities and "compounded" the incident.
PRWeek blasted the United CEO for his "tone-deaf" comments that seemed to be heavily lawyered and cast the incident "purely in terms of its effect on United, rather than the injured passenger."
"It's fair to say that if PRWeek was choosing its Communicator of the Year now, we would not be awarding it to Oscar Munoz," editor-in-chief Steve Barrett said in a column.
"Reputational risk is a huge concern for modern enterprises and relates to the value of a brand or company just as much legal and liability risk -- lawyers cannot be the first line of a communications defense."
Overbooking under scrutiny
The incident has spotlighted the common practice of overbooking and bumping passengers from flights, which airlines rely upon to avoid losing money on seats left empty by no-show passengers.
In this case, United needed to make room for a flight crew and called security personnel when no passengers volunteered to give up their seats.
A group of 21 senators on Tuesday sent a letter to Munoz announcing plans to examine the incident, and New Jersey governor Chris Christie called for the US Department of Transportation to suspend airlines from overbooking flights pending a review.
But Delta chief executive Ed Bastian called overbooking a "valid business process" that is sometimes unavoidable due to weather delays and other factors.
"It's not a question in my opinion as to whether you overbook; it's how you manage an overbook situation," Bastian said on an earnings conference call with analysts and reporters Wednesday.
Delta in 2016 had 1,200 denied boardings for the entire year, or one in 100,000 passengers. Management of the problem, which involves compensating inconvenienced travelers with gift cards of as much as $1,000 or more, was praised in some media in comparison with United's conduct.
"The key is managing it before you get to the boarding process," Bastian said. "And that's what our team has done a very effective and efficient job over."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)