United Airlines has said it will offer up to $10,000 to passengers who give up seats on overbooked flights.

The airline said it will cut back on overbooking and develop an automated system to gauge customers' interest in voluntary, compensated bumping at check-in.

The change comes as part of a review following an inquiry set up after a passenger was dragged off a fully booked United flight this month, ABC News reported on Thursday.

David Dao lost two front teeth and suffered a broken nose when he was removed from the Chicago-Louisville flight to make room for crew members in the April 9 incident.

The incident caused outrage and widespread condemnation of the airline. The shocking footage was shared and watched by millions online.

The offer by United comes after rival Delta Air Lines Inc said it will pay as much as $9,950 compared with a previous cap of $1,350 for volunteers to get off overbooked flights.

The latest incident to hit United Airlines's reputation came on Wednesday when it announced an investigation into the death of a giant rabbit which was being transported on one of its planes.

The 90-cm-long bunny, called Simon, was found dead in the cargo hold when the flight arrived at Chicago's O'Hare airport from London's Heathrow.

The company said it was striving to become a "better, more customer-focused airline" to win back the public's trust after a worldwide furore over Dao's treatment.

"Every customer deserves to be treated with the highest levels of service and the deepest sense of dignity and respect," embattled CEO Oscar Munoz said in a statement. 

"Two weeks ago, we failed to meet that standard. Today, we are taking concrete, meaningful action to make things right," he added.

Beginning on Friday, maximum compensation for voluntary denied boarding will be increased up to $10,000, said the airline.

It said there would be no more use of law enforcement officers to remove passengers from flights unless it was a matter of safety and security.

Additionally, seated passengers will not be asked to leave involuntarily and crews will be booked on flights 60 minutes before departure.

An annual training would be given to staff to handle "the most difficult situations" and customers will be paid at least $1,500 on any permanently lost bags, United said.

A "customer solutions team" will be established by June to provide gate agents with creative solutions. 

They'll explore putting passengers and flight crews on flights to nearby airports, using other airlines or providing ground transportation.