"This can never happen again on a United Airlines flight".
Munoz, who leads United's parent company, apologized again to Kentucky physician David Dao, his family and the other passengers who witnessed him being taken off the flight.
Chief executive Oscar Munoz said: "The truly horrific event that occurred on this flight has elicited many responses from all of us: outrage, anger, disappointment". The attorneys also want United's protocol for removing passengers from commercial aircraft.
Munoz told Good Morning America that he felt "shame" while watching the video of Dao being forcibly removed from the plane.
The customer who was dragged off of the United Airlines flight in a scene that triggered public fury toward the airline on Wednesday took the first step toward legal action against the carrier.
"Anyone who saw that video had the same reaction: This was completely unacceptable at every level", Emanuel said. The airline said that, when no one volunteered, the crew created a list of passengers that would be reassigned to another flight.
Speaking of his employees, Munoz said: "They all have an incredible amount of common sense, and this issue could have been solved by that".
The letter follows an incident Sunday in which United requested that four volunteers disembark from a full plane on the tarmac in Chicago to make room for company employees.
The head of the airline said this week that the security officers were following "established procedures for dealing with situations like this".
One of the officers involved in Dao's forcible removal has been placed on paid administrative duty pending an investigation leave, according to the Chicago Department of Aviation.
Three people got off the flight, but the fourth said he was a doctor and needed to get home to treat patients on Monday.
Talking to Louisville affiliate WLKY, Dao said he's recovering from his injuries in a Chicago hospital and that "everything" hurts at the moment. He refused to leave.
United Airlines will offer compensation to all passengers aboard Sunday's Flight 3411 from Chicago to Louisville, Kentucky, the airline announced Wednesday.
The US Department of Transportation is reviewing whether United complied with rules on overbooking. He issued another statement on Tuesday formally apologizing for how Dao was treated.
Videos show him being approached by security, tossed against a metal armrest and then pulled from his seat and and dragged down the aisle as he screamed and other passengers looked on in horror.