"Like you, I was upset to see and hear about what happened last night" aboard a plane about to take off Sunday from Chicago to Louisville, Munoz wrote. He said he wanted to give employees "a clearer picture of what happened."
The series of events began after the plane was fully boarded and United gate agents were approached by airline crew members who said they needed to travel on that flight, Munoz said in the memo.
"We sought volunteers and then followed our involuntary denial of boarding process," including offering compensation to anyone who would voluntarily give up their seat, the CEO wrote.
"When we approached one of these passengers to explain apologetically that he was being denied boarding, he raised his voice and refused to comply with crew member instructions," Munoz wrote.
"He was approached a few more times after that in order to gain his compliance to come off the aircraft, and each time he refused and became more and more disruptive and belligerent," the memo continued. "Our agents were left with no choice but to call Chicago Aviation Security Officers to assist in removing the customer from the flight."
The officers "were unable to gain his cooperation and physically removed him from the flight as he continued to resist," the CEO said.
Munoz said employees "followed established procedures" for such situations. Still, he said, "We are taking a close look at the circumstances surrounding this incident. Treating our customers and each other with respect and dignity is at the core of who we are."
Following the incident, one of the law enforcement officers involved was placed on leave Monday. The Chicago Department of Aviation said the officer's actions were not in accordance with standard operating procedure and are not condoned by the department.
United Flight 3411, operated by Republic Airways, was scheduled to depart Chicago's O'Hare International Airport at 5:40 p.m. local time Sunday, bound for Louisville International Airport.
United told ABC News that it had offered passengers on the plane up to $800 to give up their seats for four crew members who needed to board. No one volunteered, so the airline generated a list of four names to be removed from the flight and re-accommodated, per by the airline's contract of carriage. Three of those people complied, and one did not. That's when the police were called.
"The doctor needed to work at the hospital the next day," Twitter user Jayse D. Anspach wrote in a series of tweets accompanied by videos of the incident. "So he refused to 'volunteer.'"
Anspach added, "A couple airport security men forcefully pulled the doctor out of his chair and to the floor of the aisle. In so doing, the doctor's face was slammed against an arm rest, causing serious bleeding from his mouth. It looked like he was knocked out, because he went limp and quiet and they dragged him out of the plane like a rag doll."
ABC News has not been able to verify any details about the man who was removed, including whether he is a doctor.
According to Anspach and another passenger tweeting about the events, Tyler Bridges, the man later returned to the aircraft, repeating that he needed to go home. In video of the man after he returned, he appears agitated. Bridges tweeted that the man said he needed to be at work in the morning to see patients at his hospital.
Anspach and Bridges said in their Twitter posts that the man was bloodied from his removal.
The two declined to comment to ABC News about the alleged incident.
United would not tell ABC News what occurred to escalate the situation.
United CEO Oscar Munoz called the incident "upsetting" in a statement posted on the airline's Twitter account.
While United's rules regarding denied boarding posted on its website fall in line with Department of Transportation regulations, it is unclear what rules exist regarding passengers already on board a plane.
Though the airline did not specify why the man was chosen, United's contract of carriage, posted online, reads, "The priority of all other confirmed passengers may be determined based on a passenger’s fare class, itinerary, status of frequent flyer program membership and the time in which the passenger presents him/herself for check-in without advanced seat assignment."
United did not comment when asked why the man was allowed to board the plane.
The Department of Transportation suggests that the most effective way to reduce the risk of being bumped from a flight is to arrive at the airport early. Typically, for passengers in the same fare class, the last ones to check in usually are selected to get bumped, if necessary.
In 2016, United denied boarding at a rate of 0.43 per 10,000 passengers, according to the Department of Transportation's "Air Travel Consumer Report." American Airlines' rate was 0.64, and Delta Air Lines' was 0.10. These numbers include passengers who have confirmed reservations and are involuntarily denied boarding on a flight that is oversold.
ABC News' Dominick Proto, Whitney Lloyd and Fergal Gallagher contributed to this report.