As of Wednesday, the Chicago Department of Aviation has suspended three officers in connection with the incident pending the outcome of an investigation.
United said it is reviewing its policies, and Munoz added that the company needs a new incentive program for bumped passengers who are already seated, as in the case of Dao.
The Chicago-headquartered airline's share price fell sharply during trading on the morning of 11 April, but largely recovered during the afternoon.
Dao was on a flight from Chicago to Louisville when he and his wife were told they would need to give up their seats to make room for United staff who needed to board the flight to Kentucky.
David Dao was filmed being dragged off the overbooked flight at Chicago O'Hare airport, bloodied and screaming, in a video watched millions of times online. But newly released video of the incident doesn't appear to support the company's argument.
"No one should be treated that way", said Munoz when asked if he thought Dao was at all at fault.
Mr Munoz had initially described Dr Dao as "disruptive and belligerent". But he did an about-face days later, saying the doctor did nothing wrong. "And that's something that I've learned from". Munoz said in a letter to employees that the airline offered $1,000.
The underfire airline has also announced it will no longer use police to remove passengers from overbooked flights and will review how it goes about seeking people to voluntarily give up their seats when a flight is full.
"We are also reaching out to this passenger to talk directly to him and further address and resolve this situation".
"We followed the right procedures", Hobart said.
United Airlines spokeswoman Megan McCarthy said the passengers can take the compensation in cash, travel credits or miles. And now they were telling me I had no choice. "I have committed to our customers and our employees that we are going to fix what's broken so this never happens again". They care about their customers. "They said they have a priority list and this other person was higher on the list than me".