White House press secretary Sean Spicer on Tuesday called the forced removal of the passenger "troubling".
Bell says now that people know about these overbooking policies, United could guarantee seats to try to fix the image problem it has now.
Munoz also appeared on "Good Morning America" on Wednesday to further apologize.
The Sunday evening incident caused a furore around the world as video recorded by fellow passengers showed airport security officers yanking Dr David Dao from his seat aboard the flight. "We can't do that".
Passengers on United Express Flight 3411 will get a refund, United Airlines said Wednesday.
Megan McCarthy, a spokeswoman for the airline, declined to say if the payment would be in cash, frequent-flier miles or other forms. The passenger in question had already boarded the aircraft and was apparently one of four passengers that were randomly selected to be bumped.
Munoz said United would be examining its incentive program for volunteers on overbooked planes.
Since the video has gone viral and sparked controversy over how airlines treat their passengers, competitors Emirates and Royal Jordanian Airlines did not hesitate to throw major shade at United.
While United Airlines CEO Oscar Munozfake apologized in a public statement Monday - saying they had to 're-accommodate' Dao, aninternal letter seen by NBC News the ballyhooed CEO accused the doctor of being 'disruptive and belligerent'.
On Wednesday they filed an emergency motion in Cook County Circuit Court asking a judge to ensure the airline and city preserve surveillance video showing passengers boarding Flight 3411 to Louisville. Those documents are often the first steps toward a lawsuit.
The incident has since led to three of the officers involved in the incident being placed on administrative leave, according to the Chicago Department of Aviation.
The department announced today that two more officers have been placed on leave.
Dao can be seen in the video being dragged out of the plane with blood running down his face. United could be liable, and Dao could also sue Chicago authorities for use of excessive force, Podhurst said.
United Airlines has come under fire for dragging one of its customers off the plane after he refused to get off voluntarily. He refused to leave.
Employees then contacted Chicago Aviation Department officers to help remove Dao.
A 69-year-old passenger who did not want to give up his seat wound up being dragged off the plane by security officers. But for many, it is a case of too little, too late for many, including members of U.S. House of Representatives and the Senate, who have called for an official hearing with respect to the incident.