United Airlines faced a spiralling crisis from videos showing a passenger being dragged off an airplane, as consumers threatened a boycott of the airline and lawmakers called for an investigation.

By the afternoon, after more than a day of changing statements, United chief executive Oscar Muñoz apologised and promised a review of its policies.

"No one should ever be mistreated this way," Oscar Muñoz, the company's chief executive, said in a statement.

But the videos had already cast an unwelcome light not just on United, but on the airline industry's efforts to maximise profits. As companies push to make money from baggage fees, seat reservations and other services that were once included with a basic plane ticket, the videos added the potential for an even harsher indignity: sitting in a seat with a ticket and getting physically ejected from the airplane.

The passenger, Dr David Dao, was identified late on Tuesday in a statement from his lawyers, who said he was undergoing treatment in a Chicago-area hospital for his injuries. Some videos had showed him with a bloody face.

On social media, the firestorm swept around the world. Chinese social media users accused United, which does a lot of business in the country, of racism by targeting Dao, who appeared to be Asian. In the United States, customers showed pictures of their United loyalty or credit cards cut into pieces. And lawmakers called for an investigation.

"The degrading treatment of this individual is the latest example of a major US airline disrespecting passengers and denying them their basic rights," Sen. Richard Blumenthal, D-Conn., said in a letter sent Tuesday to the Department of Transportation.

The disturbing images of a passenger being violently ejected from an airplane by security officers come as the industry consolidates. Today, four major airlines account for about 80 per cent of domestic air travel. In recent years, as the consolidation has increased, passengers have been forced into a host of policies that ding their wallet and their comfort.

But social media has proved to be a powerful outlet for complaints. United drew quick criticism for its initial response to the Sunday evening incident, with many people calling it tone deaf. On Monday, when Muñoz apologised for having to "re-accomodate these customers," the internet saw that as a joke. "Nice to know 're-accomodate' on United now means 'drag you violently out of your seat,'" one woman posted on Twitter.

A few hours later, United seemed to go on the offensive when it circulated a letter in which Muñoz appeared to blame Dao, saying he "defied" the officers. Finally, on Tuesday afternoon, the airline changed course again, with Muñoz saying that United would take "full responsibility" for the situation.

"Better late than never, but the sentiment certainly rings a bit hollow when it follows two previous failures and 36 hours of intense public pressure," said Jeremy Robinson-Leon, a principal at the corporate public relations firm Group Gordon. "The back-against-the-wall, through-gritted-teeth apology isn't generally a winning strategy."

For United and Muñoz, who just last month was named Communicator of the Year by PR Week, a trade publication, the videos have turned into a crisis. They come on the heels of another incident about two weeks ago in which the airline was forced to defend itself about what some saw as a sexist policy after it barred two teenage girls wearing leggings from a flight.

"It's fair to say that if PR Week was choosing its Communicator of the Year now, we would not be awarding it to Oscar Muñoz," the trade publication said Tuesday.

After tumbling during the day, United's stock ended Tuesday down 1.1 per cent, stripping about about $US225 million ($299 million) off the share register.

United on Tuesday appeared to backtrack from prior statements that the flight with Dao aboard - heading from O'Hare in Chicago to Louisville, Kentucky - was overbooked.

Instead, Megan McCarthy, a spokeswoman for United, said the flight was full and then crew members, who were scheduled to operate a flight Monday morning from Louisville to Newark, New Jersey, needed seats on the plane. If the crew members had not been allowed to board, McCarthy said, the Monday morning flight would have been canceled.

Still, it is not uncommon for airlines to overbook, or sell more tickets than they have seats. At that point, they try to get people to voluntarily change their plans ??? or, if there are no takers, force them to change.

While the Transportation Department said it is investigating whether the airline complied with rules regarding overbooking, it notes that each airline sets its own system and procedures for deciding whom to bump. United said it will review its overbooking policies as well.

Many politicians also called for the rules to be reviewed. And the leading members of the Senate's commerce committee demanded a full accounting of the incident from the Chicago Department of Aviation.

Some airlines choose the passengers who paid the lowest fares, while some choose the last passengers to check in. The Department of Transportation requires airlines to give involuntarily bumped passengers "a written statement describing their rights and explaining how the carrier decides who gets on an oversold flight and who doesn't," according to its consumer guide.

While most airlines do not like to discuss how many involuntary customers they bump, Gil West, the chief operating officer of Delta, did just that in a December 2015 presentation to investors and analysts.

"This is probably the most painful customer experience you could ever have, right?" West said. "You paid for your ticket, you show up at the gate," and the airline says you can't fly, West said.

United's website says that when the airline cannot find enough volunteers, it will "deny boarding to passengers in accordance with our written policy on boarding priority." McCarthy would not share the written policy.

She said its agents follow a protocol for determining who will be selected, aiming to avoid families traveling together and unaccompanied minors. It also tends to protect people with connecting flights, those with mileage status through frequent flier or credit card programs, fare buckets and "a whole number of things," she said.

McCarthy said the protocol was followed on Dao's flight. Three passengers got off the plane. But Dao did not give up his seat and he was forcibly removed, dragged down the airplane aisle, his glasses askew, face bloodied, by several security officers.

One of the officers has been placed on leave, according to authorities.

"We recognise that our response yesterday did not did not reflect the gravity of the situation," McCarthy said. "And for that we also apologise. Our focus now is looking ahead and making this right."