The chief executive of United Airlines, Oscar Munoz, became a casualty of the public relations crisis gripping the air carrier, as the company that runs the airline said on Friday that he would not ascend as planned to the role of chairman.

The company, United Continental Holdings, is also adjusting its incentive compensation program for senior executives to make it “directly and meaningfully tied to progress in improving the customer experience.” The announcements were made in a proxy filing with the Securities and Exchange Commission.

The moves follow a public relations catastrophe that began almost two weeks ago, when a passenger was violently dragged off a United flight by a police officer before its departure from Chicago to make room for a company employee. The episode was captured by other passengers on cellphones and quickly spread on social media.

Initially, Mr. Munoz appeared to blame the passenger, Dr. David Dao, for causing the incident. But amid a backlash, Mr. Munoz changed course and said he felt “shame” over how the situation was handled.