"We are very sorry for the loss of lives", Kevin McAllister, president and CEO of Boeing's commercial aircraft, said at a press conference at the industry-wide Paris Air Show.
Speaking on Sunday before the Paris Air Show, Muilenburg told reporters that Boeing engineers learned in 2017 that a warning light in the cockpit of its top-selling Max, created to alert pilots when the two angle-of-attack sensors disagreed, didn't work as intended.
Chairman and Chief Executive Dennis Muilenburg said Boeing failed to communicate "crisply" with regulators and customers, but defended the broad engineering and design approach to nose-down control software at the center of probes into the accidents that led to the plane's worldwide grounding.
Boeing declined to comment on the report, only noting that it is "looking holistically" at "design and certification processes" in light of two 737 MAX crashes in Ethiopia and Indonesia, which killed 346 people. In April, Boeing announced plans to cut back production of its 737 MAX aircraft after several countries grounded the aircraft following the crashes.
"We clearly had a mistake in the implementation of the alert", Muilenburg said.
And Muilenburg said he was "disappointed" the company didn't reveal sooner a discovery by engineers in 2017 that cockpit alerts of certain sensor malfunctions had problems because of a software error.
Boeing and the FAA said the warning light was not critical for flight safety.
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The CEO added that he expects the 737 MAX to fly again before the end of the year.
Members of Israel's Zaka rescue and recovery team at the crash site of the Ethiopian Airlines Boeing 737 Max 8 jet south of Addis Ababa March 12, 2019.
He said a possible new jet dubbed NMA had fallen behind the MAX's return to service as a priority, but that the timeline on decisions and entry to service remained unchanged.
Mr Muilenburg called the crashes of the Lion Air and Ethiopian Airlines jets a "defining moment" for Boeing, but said he thought the result would be a "better and stronger company". The pilots were unable to regain control of the aircraft.
The two crashes - one in October and another in March, both killing everyone on board - plunged Boeing into its deepest crisis in decades after regulators grounded the aircraft globally.
"We haven't given the airlines a specific timetable", Muilenburg said. But Airbus has outpaced Boeing in selling planes in this category.
Muilenburg projected that within 10 years, the overall aviation market - including passenger jets, cargo and warplanes - would be worth $8.7 trillion, compared to earlier forecasts of $8.1 trillion.