Muilenburg said Boeing is examining the design and operation of the 737 Max and will make any appropriate changes.
Boeing said Monday that the flight stabilization system under scrutiny following two deadly 737 MAX plane crashes, met all United States regulations.
The letter comes as Boeing and the U.S. regulator have been under media fire for their handling of the crashes: Lion Air Flight 610 in Indonesia, which killed 189 people in October, and Ethiopian Airlines Flight 302, which killed 157 on March 10.
While the causes of both crashes are unclear, suspicions have grown around a software system developed for Boeing's latest Max planes.
"We know lives depend on the work we do", Mr Muilenburg said.
The motors on the new plane are heavier than in the 737 NG, posing more of a risk of stalling, so the MCAS was created to protect against the possibility.
The U.S. government, Boeing, airline officials and others are examining the crashes.
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Boeing did not immediately return a request for comment from Reuters.
In service since May 2017, the 737 MAX 8, one of several variants of the 737 MAX, has now experienced two deadly tragedies, a scenario that is unprecedented for a new aircraft.
"If that's the case, that does raise the possibility that there is a similar occurrence between the Lion Air and Ethiopian Airlines accidents", said Clint Balog, a Montana-based professor at Embry-Riddle Aeronautical University.
Boeing CEO Dennis Muilenburg said Monday a software update and related pilot training for the 737 MAX will be released "soon" and will address concerns discovered in the aftermath of the Lion Air crash.
"During the verification process of the FDR (Flight Data Recorder) data, clear similarities were noted by the investigation team between Ethiopian Airlines Flight 302 and Lion Air Flight 610, which will be the subject of further study during the investigation", the BEA said in a statement.
Boeing jets were featured on a draft list of American products China would buy to reduce its trade surplus with the US, the people said, asking not to be identified discussing private deliberations.
Shares of Boeing dropped another 1.8 percent on Monday to $372.28.
- US lawmakers said the planes could be grounded for weeks to upgrade and install the software in every plane.