He also expressed regret for initial statements in the days following the incident that appeared to blame Dao for the incident. In a letter to employees that was leaked to CNBC, Munoz said Dao was "belligerent".
"My initial words fell short of truly expressing what I was feeling," he said. "That is something that I've learned from."
In pledging a full investigation into the matter, Munoz also hinted that there will be changes in the way local law enforcement deals with passengers aboard United flights. When Dao refused to leave the flight voluntarily, police were called to remove him.
"The use of law enforcement aboard an aircraft has to be looked at very carefully," Munoz said. "That is a policy that we absolutely have to look at."
At least one of the officers involved in the incident has been placed on paid leave as the investigation into the incident continues, according to the Chicago Department of Aviation. Munoz said United will release the results of its internal investigation by April 30.
Videos shot by passengers aboard the Louisville-bound flight from Chicago's O'Hare International Airport show Dao screaming as he is dragged down the aisle of the plane and again a few minutes later when he returns to the plane. Dao's face is bloody and his clothing mussed. When asked his reaction to seeing the footage, Munoz said "shame" was among the words that came to mind.
Attorneys for Dao, said Tuesday that he remains hospitalised in Chicago, undergoing treatment for his injuries.
"The family of Dr Dao wants the world to know that they are very appreciative of the outpouring of prayers, concern and support they have received," Chicago attorney Stephen L. Golan said in a statement.
The incident has raised hopes among passenger advocate groups such as FlyersRights.org, that Congress may act on reforms to make air travel more consumer friendly.
The video has indeed caught the attention of members of Congress, many of whom are frequent fliers. Nearly a dozen members of Congress have sent letters to United, officials at O'Hare and the US Department of Transportation demanding an explanation for why Dao was forcibly removed from the plane. DOT officials said its office of Aviation Enforcement and Proceedings is currently reviewing the matter. They noted that the flight was operated by one of United's regional partners, Republic Airlines.
Senator Chris Van Hollen announced he is seeking support for the "Customers Not Cargo Act," which would prohibit airlines from forcibly removing passengers after they have already boarded the plane due to overbooking or airline staff seeking to fly as passengers.
"We were all shocked and outraged this week when United Airlines forcibly and brutally removed Dr David Dao from Flight 3411," Van Hollen wrote to his colleagues. "...we should act immediately to ensure that airlines cannot force passengers who have already boarded to leave the plane in order to free up seats for others. Instead, they must provide sufficient incentives to encourage passengers to voluntarily deplane."
New Jersey Governor Chris Christie also joined the fray, saying on CNN that he has asked the Trump administration to prevent airlines from overbooking flights until new guidelines are put into place.
"This is unacceptable - to have somebody pay for a ticket, reserve a seat, be seated and dragged off the plane physically by law enforcement officers by the direction of United. It's outrageous," Christie told CNN's Alisyn Camerota on New Day. "That's why I've asked the Trump administration to stop overbooking until we set rules how the airlines can conduct themselves."
But the Trump administration may be loathe to get involved. During a briefing on Tuesday, Press Secretary Sean Spicer said that while the video was "troubling" he dismissed calls for a federal investigation into what he said should be "a very local matter".
The situation has indeed focused attention on airlines' practice of overbooking, in which it sells more tickets than seats to compensate for travellers who don't show up for their flights. Such a practice, is not illegal, but can lead to conflict if there is a mismatch between passengers and seats.
A United spokesman clarified earlier statements to say that the flight, which Dao was booked on was not overbooked. In reality, the airlines wanted the seats for four crew memberss who needed to get to Louisville by Monday so they could staff another flight the next morning.
This is the second time in less than a month that United has been called out for its treatment of passengers. Late last month, a traveller at Denver International Airport witnessed an exchange in which it appeared that an agent was barring two teenage girls from boarding because they were wearing leggings.
The traveller tweeted about the incident which set off a firestorm in the Twitterverse. It turned out that the girls were travelling on company passes, which require them to abide by United's dress code. But the airline's delayed response only fuelled the idea that it didn't care about its customers.
In the wake of the two incidents, some have called for Munoz to step down from the job he had held since September 2015. But Munoz said he will remain United's chief.
Said Munoz: "I was hired to make United better and we've been doing that and that's what I'll continue to do."
