A United Airlines spokesperson told the agencies that the passengers "are receiving compensation for the cost of their tickets".
Munoz spoke three days after a passenger was dragged off a plane, bloodied and screaming, by authorities at Chicago O'Hare International Airport.
The airline offered passengers up to $800 to give up their seats before it began choosing people to leave, according to other passengers.
On Wednesday morning, in an interview with ABC's Good Morning America, Munoz said he felt "ashamed" when he saw the videos.
Munoz - who last month was named "US Communicator of the Year" by PR Week - pledged a "thorough review" of the airline's procedures and said the carrier would not send law enforcement officials onto planes remove passengers.
However, after the video first emerged, Munoz had described Dao as "disruptive and belligerent" before changing his tune on Tuesday and issuing the apology. Additional information from a April 13 news conference revealed that his wife was not selected.
Demetrio says Dao will "probably" sue over the incident and that the city of Chicago, which employs the guards, is also responsible. But once they found out that the next flight wasn't until Monday afternoon, he demurred and sat back, saying he was a physician who needed to get to work the next day.
The doctor dragged off of a United Airlines flight this week filed an emergency bill of discovery in Cook County Circuit Court on Wednesday asking for the court to order United and Chicago to preserve evidence of the incident that went viral.
The video also underscores a growing dilemma: From airlines to schools, police are called to deal with situations that in the past might have been handled without them, sometimes leading officers to respond with force far beyond the provocation. Dao, though, refused to be bumped and was dragged off the plane by armed police - in full view of other passengers and their smartphones.More news: North Korea attempts but fails to launch missile - South Korea
"That is not who our family at United is", Munoz said.
Dao's daughter, Crystal Dao Pepper, said the family was "horrified, shocked and sickened" when they learned what happened to Dao on the plane. Sometimes it happens because the airline needs room for employees who are commuting to work on another flight - that's what happened Sunday on United Express.
The department released the following statement: "The Chicago Department of Aviation (CDA) continues reviewing the details surrounding the incident".
The airline's chief executive, Oscar Munoz, is insisting he will not resign.
"Once a plane is boarded, no one should be asked to leave", she said.
The Monday incident comes two weeks after United drew social-media scorn for enforcing its employee dress code for those who fly as non-revenue passengers, such as relatives of employees.
It's an often-overlooked policy to which you agree when you book your tickets.
Sen. Richard Blumenthal, D-Conn., asked the U.S. Department of Transportation to analyze "the problem of overbooking passengers throughout the industry".