Boeing has conceded that new software added to the MAX and called MCAS was involved in both crashes but questions have also been raised about the actions of the flight crews.
Boeing said last week it would cut monthly 737 MAX production by 20 percent starting mid-April, without giving an end-date.
The family of a Minnesota man who died when an Ethiopian Airlines plane crashed last month has filed a wrongful death lawsuit against Boeing, the manufacturer of the 737 Max aircraft that was involved in the crash and is now being investigated by USA prosecutors.
China was the first to ground the newest version of Boeing's workhorse 737 model last month following the Ethiopian Airlines crash, prompting a series of regulatory actions by other governments worldwide.
Many analysts believe the deliveries will only be delayed, not lost forever, unless airlines cancel orders for the plane.
"Boeing's CEO explicitly apologised to 346 passenger families", said Merdian Agustin, whose husband died in the crash. Pilots on each flight fought unsuccessfully to regain control, according to flight data retrieved from the planes. Boeing hasn't described the second issue but says it is not related to the anti-stall system.
Smaller rival Southwest Airlines was the first United States airline to cut formally its financial outlook for the year after being forced to pull its new fleet of 34 Max planes out of service.
"We are in close communications with Boeing, and there is no change on the orders for the moment".
The FAA faces a number of investigations into the certification of the plane amid allegations it was too close to Boeing.
There were more than 300 Max jetliners in operation at the time of the fatal Lion Air crash last October, and about 4,600 more on order.
At Boeing, Muilenburg said a software fix is on the way. "I expect that to be a hiccup". On Tuesday, American Airlines cut a key revenue estimate after canceling 1,200 flights in the first quarter due to the grounding of its 24 Max jets.
Shares of Chicago-based Boeing fell $5.48, or 1.5%, to close at $369.04.
American Airlines also said that it was unable to forecast how much the disruption would cost the company.