Now, after being widely criticized for his initial response to the incident, United's CEO is acknowledging that the viral video represents a "watershed moment" for the airline.
Dao, who was forcibly removed from his seat by airport police to make room for a crew member, suffered a concussion and broken nose and lost two front teeth, according to his attorney.
Initially, Munoz defended the airline's actions, labeling Dao "disruptive and belligerent" and claiming employees "followed established procedures" while attempting to "re-accommodate" the 69-year-old doctor.
The reaction was swift and severe.
In a follow-up interview with ABC News' Rebecca Jarvis, Munoz apologized to Dao and acknowledged that he was "ashamed" of the video.
"He was a paying passenger sitting on our seat in our aircraft and no one should be treated that way, period," Munoz told Jarvis. "This is not who we are."
"He apologized -- we accept that," Dao's attorney, Thomas Demetrio, told reporters. "But that's not going to let him off the hook here."
"Bullying customers has gone to the next step," he added. "Are we all going to be treated like cattle?"
In his latest statement, released alongside the airline's first-quarter earnings report, Munoz said the company is "more determined than ever to put our customers at the center of everything we do."
In the aftermath of the Dao incident, United indicated that it changed its policy to prevent crew members from displacing any customers who are already seated on a plane.
ABC News' Whitney Lloyd, Jeffrey Cook, and Taylor Dunn contributed to this report.