Oscar Munoz said he “continues to be disturbed” by the incident, captured on a video that went viral on Twitter.
He said the company would “fix what’s broken so it never happens again”.
The family of the passenger, David Dao, issued a statement expressing gratitude for the “outpouring of support”.
He is undergoing treatment at a Chicago hospital.
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 fully booked, United spokesman Jonathan Guerin told USA Today newspaper. The airline wanted to get four passengers to leave the flight to make room for four staff members who were needed in Louisville the next day.
United had previously described the flight as overbooked.
Three passengers agreed to leave the plane.
But Dr Dao 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, also emerged online.
Earlier, Mr Munoz had 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”.
The statement released on behalf of Dr Dao said the family “wants the world to know that they are very appreciative of the outpouring of prayers, concern and support they have received”.
It said the family was at present only concerned with Dr Dao’s medical care and would not be making further statements until he was discharged.
One of the aviation security officers involved in removing Dr Dao from the plane has been “placed on leave”, the Chicago Department of Aviation said, and his actions were “obviously not condoned by the department”.
It also said it would carry out a review into the incident, which it said was “not in accordance with our standard operating procedure”.
The US Department of Transportation is reviewing whether United complied with rules on overbooking.
US media say David Dao is a medical doctor from Elizabethtown, Kentucky.
United earlier said it was trying to talk to him directly in order to “further address and resolve this situation”.
Stock in United Continental Holdings dropped by more than 4% at one point with nearly $1bn (£800m) wiped off its value, but the share prices later recovered and were down just 1% when markets closed.