United Airlines chief executive Oscar Munoz on Tuesday took personal responsibility for an incident last month in which a passenger was battered and dragged from a flight, saying at a congressional hearing, “We had a horrible failure three weeks ago.”

Munoz again apologized personally to David Dao, the passenger who boarded a United plane in Chicago and then refused to give up his seat when the airline needed it to accommodate crew members. Police were summoned, and Dao, 69, was dragged bloodied from the flight as other passengers captured the scene on video.

“There will come a day when Americans won’t accept your apology,” said Rep. Michael Capuano, D-Mass., during the hearing before the House Transportation Committee. “We have a problem. It shouldn’t be as bad as it is.”

Committee Chairman Bill Shuster, R-Pa., said that “there’s something clearly broken when passengers have been treated the way they have.” Shuster warned airlines to “seize the day” because if carriers do not reform their passenger policies, Congress will impose rules, and “you’re not going to like it.”

Rep. Peter DeFazio, D-Ore., the panel’s ranking Democrat, said passenger rights have gotten short shrift as the industry has consolidated into four major carriers that handle 80 percent of flights. DeFazio said 40,000 ticketed passengers were bumped from their flights last year. “Very few passengers have any idea what their rights are,” he said.

Munoz acknowledged United’s failures in his opening statement.

“We called law enforcement when a safety or security issue did not exist,” he said. “We rebooked crew at the very last minute. We didn’t offer enough compensation or travel options to incentivize a passenger to give up a seat. And, most important, our employees did not have the authority to do what was right for our customers.”

Last week, the airline released the results of an internal investigation into the matter, saying it had failed on multiple fronts and promising changes in an effort to win back the public’s trust. That same day, it also announced it reached a confidential settlement with Dao, a Kentucky physician.

Tuesday’s hearing showcased stark differences between how airline executives and their customers view the state of the industry. While executives bragged that they are losing fewer bags, have improved their on-time performance and are offering consumers a better flight experience with more choices and cheaper fares, members spoke of calls from angry constituents who said they had been bumped, delayed and treated with indifference when they tried to complain. Members griped about smaller seats and the lack of choices when it came to booking their own flights home.

In addition to two hearings this week, Dao’s ordeal has prompted a flurry of legislation, including a bill that would ask the secretary of transportation to review the practice of overbooking and whether there should be limits on the number of seats an airline can sell on a flight.

It was a long day for airline executives, and United’s Munoz in particular, who called Dao’s forced removal “a mistake of epic proportions.”

Perhaps the best line of the day came from Rep. Rob Woodall, R-Ga., who quipped: “You know you’re having a bad day when the group that lectures you on customer service is Congress.”

The executives did have their allies, who blamed government overregulation for creating some of the problems and Dao for not listening to aviation security officers who ordered him to leave the flight.

Much of the focus, however, was what actions airlines are taking to prevent a repeat of Dao’s violent encounter.

Munoz reiterated his pledge that the dragging incident would prompt a “culture change” at United, starting with a new focus on the customer. He said United would reduce its reliance on overbooking and now offer up to $10,000 in flight vouchers to fliers who give up an overbooked seat. He also said that no passengers who have been seated would be asked to leave the airplane, except in situations involving security or safety.

Munoz was joined by United President Scott Kirby, who defended overbooking as necessary in some situations.

“We view overbooking where we can incentivize a customer to take an alternative flight as a win-win situation for both the airline and those customers,” Kirby said, “and 96 percent of the incidents where we have an overbooking we were able to get customers to be volunteers [to take another flight]. And in today’s world, where we’re increasing the compensation to $10,000, we hope to drive that down to zero.”

The four Chicago Department of Aviation officers involved in the April 9 incident at O’Hare International Airport have been suspended for their handling of Dao. The head of the Chicago Aviation Authority, Ginger Evans, is expected to testify at a Senate hearing Thursday.

United was not the only airline that had to answer for recent episodes involving passengers.

Officials at American Airlines again apologized for an April 21 incident that involved a flight attendant who allegedly tried to pull a baby stroller away from a customer who was holding a baby. A video of the incident shows the mother in tears as another passenger confronts the flight attendant.

American publicly apologized in the aftermath, removed the flight attendant from service and upgraded the woman and her family to first class for the balance of her international flight.

“It shouldn’t take a media event or a viral social-media outcry to get executives in this industry to rethink how they treat their customers,” said William J. McGee, an aviation consultant with the Consumers Union.