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".
BBC