United Airlines struggled on Wednesday to respond to a third day of public outrage over widely shared videos of a passenger being dragged off an airplane, offering a refund to every passenger on the flight and promising to no longer have the police remove passengers from planes that are too full.

The city of Chicago, where the episode occurred on Sunday, also continued to act. Two more officers from its Department of Aviation who were involved in the violent removal of the passenger — Dr. David Dao, 69, of Kentucky — were placed on administrative leave while investigators continued “reviewing the details surrounding the incident,” said Karen E. Pride, a spokeswoman for the department. One officer had been placed on leave on Monday.

On Wednesday, lawyers for Dr. Dao asked an Illinois court to order United to preserve surveillance footage, a cockpit voice recording and other information related to the flight, and they announced a news conference with a daughter of Dr. Dao would take place Thursday morning in Chicago.

Dr. Dao was left with a bloodied face when he was forcibly removed from United Express Flight 3411 from Chicago to Louisville, Ky., after the already seated passengers were told that four of them would need to leave the flight to make room for United employees. He received treatment for his injuries, the extent of which were not clear, at a Chicago hospital after he was removed from the plane.