Oscar Munoz said he felt "shame and embarrassment" and vowed it would never happen again to a seated passenger on one of United's overbooked aircraft.
The embattled aviation boss said the passenger in question, David Dao, deserved "certainly an apology".
Mr Munoz initially described Mr Dao as "disruptive and belligerent".
"That shame and embarrassment was pretty palpable for me and for a lot of our family," the contrite chief executive told ABC's Good Morning America programme.
Asked if he would stand down, Mr Munoz said: "No. I was hired to make United better and we've been doing that and that's what I'll continue to do."
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