NEW YORK (Reuters) - The backlash against the rough removal of a United Airlines (>> United Continental Holdings Inc) passenger to make room on a crowded flight has opened a divide in the U.S. industry over how to manage flight overbooking, with some renouncing the practice and others offering richer incentives to give up seats.

Overbooking is likely to be on the agenda when members of Congress hold hearings on industry behavior in coming weeks. The House Transportation Committee has summoned United Chief Executive Oscar Munoz to testify at the hearing aimed at determining "what can be done to improve the flying experience."

United on Thursday increased its maximum incentive to $10,000 for volunteers on overbooked flights. The Chicago-based carrier also said it aimed to reduce overbooking and decrease instances of involuntary denied boarding to "as close to zero as possible."

United on Thursday agreed to a settlement, with undisclosed terms, with Dr. David Dao, 69, who was dragged down the aisle of a plane in Chicago on April 9.

Southwest Airlines said on Thursday it would no longer overbook flights. The company had the highest forced bumping rate among large U.S. carriers in 2016, according to Transportation Department data.

Prior to the United incident, just one of the major U.S. carriers, JetBlue (>> JetBlue Airways Corporation), had a policy explicitly stating it would not overbook flights.

Some lawmakers have called for new airline regulations. By taking voluntary steps, carriers could deflect harsher scrutiny, as automakers have done in the past when confronted with safety scandals.

Overall, U.S. airlines are relying less on bumping passengers from overbooked flights, even as they increase the share of occupied seats.

According to a Reuters analysis of Department of Transportation data, the largest U.S. airlines have increased their domestic and international load factor, which measures how many seats are actually occupied by passengers, to 84 percent in 2016 from 80.8 percent in 2010.

In the same period, carriers also decreased the rate of passengers denied boarding on overbooked flights by more than 42 percent from 2010 to 2016.

Other airlines, including Delta Air Lines (>> Delta Air Lines, Inc.), did not renounce overbooking. But Delta increased its maximum passenger incentive to $9,950.

American Airlines (>> American Airlines Group Inc), the world's largest carrier, updated its conditions of carriage to state that it would not "remove a revenue passenger who has already boarded in order to give a seat to another passenger." The company has not announced other changes to its sales practices.

In a post-earnings call after the United incident, Delta Chief Executive Officer Ed Bastian defended the company's policy on overselling flights, arguing that implementation, not the practice itself, was the problem.

"Overbooking is a valid business process," Bastian said. "It's not a question, in my opinion, as to whether you overbook; it's how you manage an overbook situation."

(Reporting by Alana Wise and Grant Smith; Editing by Richard Chang)

By Alana Wise and Grant Smith