Dozens of countries, including the United States, and airlines have grounded the MAX 8 in the aftermath of last week's crash of an Ethiopian Airlines plane, which killed all 157 people aboard.
It was only days later that US President Donald Trump announced the grounding of all Boeing 737 MAX 8s.
The other fatal plane crash happened in October when a Lion Air flight went down, crashing into the Java Sea, killing 189 people.
Boeing and USA aviation regulators are coming under intense scrutiny over the certification of the 737 Max aircraft after news that two recent crashes share similarities.
A week after a Boeing 737 Max 8 passenger jet crashed in Ethiopia, that country's transport minister said recovered flight recorders from Ethiopian Airlines Flight 302 showed "clear similarities" to a deadly accident in Indonesia last October involving a Lion Air plane of the same model.
At least a portion of the flight-control software suspected in the 737 Max crashes was certified by one or more Boeing employees working in an outsourcing arrangement.
The probe is focusing on the Manoeuvring Characteristics Augmentation System, or MCAS, implicated in the Lion Air crash, which authorities have said shared similarities with the latest accident.
After a 10 percent drop last week that wiped almost $25 billion off its market share, Boeing stock slid about 1.8 percent on Monday.
With the prestige of one of the United States' biggest exporters at stake, Boeing has halted deliveries of its best-selling model that was meant to be the industry standard but is now under a shadow. In the Lion Air crash, sensors possibly misread the plane's performance and sent the jet into a dive to avoid a phantom stall.
Did any element of the design or certification process for the 737 Max introduce a risk factor?
The FAA last week said it already had ordered Boeing to develop a fix for problems with the MCAS system.
Muilenburg emphasised, however, that the company would continue to providing "the best products, training and support to our global airline customers and pilots, pursuant to an ongoing and relentless commitment to make safe airplanes even safer". Engineers with the FAA reportedly did not read technical documents submitted by Boeing.