Videos taken by other passengers on the same flight drew more than a million hits on social media, with many criticizing United Airline's handling of the incident.
U.S. President Donald Trump said it was "horrible" that Dao was dragged off the flight, according to an interview from the Wall Street Journal.
United was asking passengers to give up their seats voluntarily for compensation as four crew members needed to get on the flight in order to work another one in Louisville or else that flight would be canceled, airline spokeswoman Maddie King said.
After incentives of up to $800 (£640) failed to convince anyone to leave, the airline said the computer would choose which passengers would go.
But facing a PR disaster on Tuesday evening, Munoz issued a new statement saying he "continues to be disturbed" by what happened and the airline would "fix what's broken so it never happens again". "We're not going to put a law enforcement official... to remove a booked, paid, seated passenger", Munoz said.
Editor's note: A previous version of this story indicated that Dao and his wife were two of four passengers selected by the airline to be removed.
Paul Callan, a civil and criminal trial lawyer in NY, said the public outcry over Dao's treatment would likely push the airline to a quick and generous settlement.
One of the officers could be seen grabbing the screaming man from his window seat, across the armrest and dragging him down the aisle by his arms.
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That's what happened on a United flight Sunday leaving Chicago O'Hare International Airport. The man has been identified as David Dao of Kentucky, according to local news station WLKY.
The aviation security officer who pulled the man from his seat was placed on leave Monday, "pending a thorough review of the situation", the Chicago Department of Aviation said in a statement. He said he took full responsibility for the situation but has no plans to resign. No one explained why four airline employees showed up without notice, needing seats that already were occupied by fare-paying passengers.
Aviation Commissioner Ginger Evans says the officers had the authority to board the plane but that the rest of what occurred is under investigation. Blood is on his mouth, chin and cheek as he said: "I want to go home".
Airlines have broad discretion to eject people from flights for almost any reason, a consumer advocate tells NPR.
When no-one volunteered, a United manager came on the plane and announced that passengers would be chosen at random.
Munoz's latest statement described the removal as "truly horrific".
Royal Jordanian tweeted a no-smoking picture saying "drags on our flights are strictly prohibited by passengers and crew".
The executive's initial response to the incident lacked an apology to Dao. Powell said Dao was naturally annoyed as he was asked to give up his seat, but was not at all belligerent.