DALLAS >> United Airlines says it will raise the limit — to $10,000 — on payments to customers who give up seats on oversold flights and will increase training for employees as it deals with fallout from the video of a passenger being violently dragged from his seat.

United is also vowing to reduce, but not eliminate, overbooking — the selling of more tickets than there are seats on the plane.

The airline made the promises Thursday as it released a report detailing mistakes that led to the April 9 incident on a United Express plane in Chicago.

United isn’t saying whether ticket sales have dropped since the removal of a 69-year-old passenger by three airport security officers, but the airline’s CEO admits it could be damaging.

“I breached public trust with this event and how we responded,” Oscar Munoz told The Associated Press. “People are upset, and I suspect that there are a lot of people potentially thinking of not flying us.”

To head off customer defections, United had already announced that it will no longer call police to remove passengers from overbooked flights, and will require airline crews traveling for work to check in sooner. On Thursday, it added several other new policies including:

— Raising the limit on compensation to $10,000 for customers who give up their seats. That is a maximum — it’s unclear how many, if any, passengers would see that much. The current limit is $1,350. Delta Air Lines earlier this month raised its limit to $9,950.

— Sending displaced passengers or crew members to nearby airports, putting them on other airlines or arranging for car transportation to get them to their destinations.

— Giving gate agents annual refresher training in dealing with oversold flights. Munoz said he also wants agents and flight attendants to get more help at de-escalating tense situations.

For United, the timing of the viral video could hardly have been worse. The airline struggled badly after a 2010 merger with Continental, enduring several technology breakdowns that angered customers. In the past year, however, the airline has flown more on-time flights and lost fewer bags. It recently rolled out plans for expanding service this summer.

Instead of being commended for those signs of progress, however, it has faced more than two weeks of withering criticism and mockery. David Dao, the passenger injured when he was yanked from his seat, is almost certain to file a lawsuit.

Munoz apologized again and faulted his own initial response, in which he defended airline employees and called Dao belligerent.

“That first response was insensitive beyond belief,” Munoz said. “It did not represent how I felt,” saying that he got “caught up in facts and circumstances” that weren’t initially clear, instead of expressing his shock.

In Thursday’s report, United provided new details about the incident. It said Flight 3411 to Louisville, Kentucky, was oversold by one ticket, but a volunteer gave up his seat. After passengers boarded, four crew members of Republic Airline, which operates many United Express flights, showed up late after their Louisville-bound plane was delayed by a mechanical problem.

United said it was a mistake to let the Republic crew board late, which required removing four paying passengers; calling officers when there was no safety or security issue; and not offering enough money to entice volunteers to give up their seats.

“We could have spent a lot of $10,000s and made that thing right,” Munoz said.

United said it will reduce but not end the overbooking of flights. Munoz said if airlines can’t overbook flights there will be more empty seats and fares will rise. Delta CEO Ed Bastian called overselling flights “a valid business process.”

Politicians in Washington and elsewhere have called for a ban on overselling flights. Some critics have said airlines should leave a few seats empty if they think they will be needed by crew members.

“This overbooking needs to be softened,” Dao’s attorney, Thomas Demetrio, told the AP. “People really do believe when they buy their ticket they are good to go.”