On the call, United Airline chief executive Oscar Munoz said he would have "further conversations with customers and related governmental officials" in an upcoming trip to China that had been planned prior to the incident.
Mr Munoz, who initially backed claims that Dr Dao was "belligerent" and "disruptive", said: "I'm sure there was lots of conjecture about me personally".
Dao received a concussion and a broken nose and had two of his teeth knocked out. It has also said it will now require that crew members taking flights to be booked at least an hour before the flight.
Mr Munoz's early statements on the incident were widely criticised.
United signaled on Sunday that it will no longer let its staff take the seats of already boarded passengers on overbooked flights.
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"The incident has been a humbling learning experience for all of us here at United", he said.
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United is under fire from both the Chinese and Vietnamese communities for its treatment of 69-year old Dr. David Dao, who was violently removed from his seat after being one of four passengers randomly selected due to an overbooking issue.
Dao emigrated to the USA from Vietnam.
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It is a special honoring for the Patriots team, and a reminder of what they accomplished. Six other Patriots had announced they wouldn't attend the event for political reasons.
"We've always thought to repay our customers" trust with the highest quality of service and deepest level of respect and dignity, ' Munoz said.
It has already triggered calls for a boycott of the airline by Asian groups in the U.S., as well as in Vietnam and China.
Asked if there was a drop in bookings from China, where video of the incident provoked widespread outrage, Kirby said it's too early to say because there are too few days to measure possible changes.
In the conference call, company leadership unequivocally said it was impossible to tell whether air traffic had declined in the wake of the recent public relations debacle, especially given the time frame, as the week before the Easter holiday generally yields lower traffic.
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And their own second goal in Madrid may also have been - fractionally. "One year of hard work, thank you referee, bravo!" was the caption on one of his photos.