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".
Munoz added, "The first thing is to apologize to Dr. Dao, his family, the passengers on his flight", he said.
The United CEO issued an apology to all of its passengers over how this whole fiasco played out, but then he also said he "emphatically" stands behind his employees.
United spokeswoman Megan McCarthy said Wednesday that the passengers can take the compensation in cash, travel credits or miles.
US Senator Chris Van Hollen, a Maryland Democrat, announced plans for the Customers Not Cargo Act, which would prohibit the forcible removal of passengers already aboard an aircraft "due to overbooking or airline staff seeking to fly as passengers".
By Tuesday afternoon, nearly two days after the Sunday evening events, Munoz issued another apology.More news: Jimmy Fallon On Going Live Coast To Coast For The First Time
In the last two days after Sunday's incident went viral, may airlines have taken a shot at the USA carrier.
He said that going forward United will not put law enforcement officials on planes in order to remove a "booked, paid, seated passenger".
Dao told WLKY, a local Kentucky station, on Tuesday that he was still being treated at a Chicago hospital for injuries he suffered.
The others complied. After Dao refused, airport security officers yanked him out of his seat and dragged him off the plane. Three of the officers involved in the situation are now on leave.
"Normally if you are somebody that they don't have a seat for one reason or the other, they will just walk with you...but security doesn't have to do that".
Mr Munoz, recently named US Communicator of the Year 2017 by PRWeek magazine, said: "I want you to know that we take full responsibility and we will work to make it right".