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7 year oldOscar Munoz said he "continues to be disturbed" by the incident, during which a passenger was forcibly dragged, screaming, off a plane.
He said the company would "fix what's broken so it never happens again".
United's parent company's share price plummeted on Tuesday after a video of the incident went viral on Twitter.
Stock in United Continental Holdings dropped by more than 4% at one point on Tuesday, and at one point nearly $1bn (£800m) was wiped off its value - but share prices later recovered and were down just 1% when markets closed.
The footage taken inside the airliner shows a man being pulled out of his seat and dragged, screaming, down the aisle. He is later seen with blood on his face.
The flight from Chicago to Louisville, Kentucky, on Sunday evening had been overbooked - a fairly common practice - so the airline wanted to get four passengers to leave the flight to make room for four staff members.
United Airline's public relations disaster
Three passengers agreed and left the plane. But the man said he worked in a hospital, and needed to see his patients the next day, an eyewitness tweeted.
A video that appears to show him dazed and with blood around his mouth, saying "just kill me", having run back on the plane, has also emerged online.
Earlier, Mr Munoz defended employees' conduct and said the passenger had been "disruptive and belligerent". Employees were "left with no choice but to call Chicago Aviation Security Officers to assist in removing the customer from the flight", he added.
He came under intense criticism online and the incident reached the ears of the White House press secretary, Sean Spicer, who called it "troubling".
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