In a letter to employees, Oscar Munoz said he was "upset to see and hear about what happened".
But he said that the passenger had been "disruptive and belligerent".
The airline earlier said that it was investigating what happened after videos provoked a social media outcry.
The footage taken inside the airliner shows a man being pulled out of his seat and dragged down the aisle. He is later seen with blood on his face.
The man has not been officially identified but a passenger who sat next to him told BBC Radio 5 Live that he said he was originally from Vietnam and had been living in Louisville, Kentucky, for about 20 years. He said he and his wife were both doctors.
The flight from Chicago to Louisville on Sunday evening had been overbooked.
The airline wanted to get four passengers to leave the flight to make room for four staff members.