The Chicago-based United Airlines airline is reviewing policies with regard to handling oversold flights to prevent similar incidents, and talking to some passengers and employees on how the airline can take a more "common-sense approach".
Mr Munoz and other executives vowed to treat customers with dignity, and said that what happened to Dr Dao will never happen again.
Dao received a concussion and a broken nose and had two of his teeth knocked out.
United Airlines' reputation is circling the drain after the forcible removal of a passenger from one of its flights went viral and made worldwide headlines last week.
Many lawmakers fly home almost every week while Congress is in session, so the United incident hit a raw nerve.
The violent removal of a passenger on a United Airlines flight has prompted US Senator Richard Blumenthal to propose a new passengers Bill of Rights that would mandate compensation for travellers involuntarily "bumped" from their airline seats.
The company's first-quarter profits outperformed the expectations of financial analysts, and Munoz said it gave the carrier "a lot of confidence" going forward, the Tribune reports.
New Zealand braces for Cyclone Cook
It is due to hit New Zealand's North Island later today, with wind gusts of more than 150 km/h possible. Air New Zealand canceled flights across the country.
'It's never too late to do the right thing, ' a statement from Munoz read.
It's not yet clear how the April 9 incident with Dao, which Munoz said occurred due to a "system failure across various areas", will affect the company's business, although the airline's stocks have fallen 3%, losing the company $673 million in market value.
Last week, United announced that it will no longer call police to remove passengers from overbooked planes.
The company is now conducting a review of its policies on overbooked flights - with details expected later this month.
The airline suffered a public relations disaster after a video emerged a week ago showing security officers dragging a bloodied passenger off an overbooked United Express flight in Chicago.
"It's really too early for us to tell anything about bookings and in particular last week because it was the week before Easter, that's normally a very low booking period", said United President Scott Kirby.
"I want to know why this happened, how it was allowed to occur and what protocols are in place to handle overbooked flights", said Rep. Rodney Davis, R-Ill.
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