Boeing Co's chief executive said on Thursday that about two-thirds of the planemaker's 737 MAX customers have joined simulator sessions with a software update designed to prevent disasters like two recent fatal crashes involving its best-selling jetliner.

In his first public speech since an Ethiopian Airlines 737 MAX crash that killed all 157 aboard on March 10, Boeing CEO Dennis Muilenburg said additional tests are expected in the coming weeks as the planemaker works to regain the confidence of its customers and the flying public.

Boeing, fighting its biggest crisis in years, has been developing an upgrade to software that is under scrutiny in the Ethiopian Airlines accident and a Lion Air 737 MAX crash that killed all 189 on board on Oct. 29.

The world's largest planemaker is under pressure to convince MAX operators and global regulators that the aircraft, which was grounded worldwide in March, is safe to fly again.

Muilenburg did not indicate when Boeing will deliver the software fix to international regulators for their review, which is expected to last around 90 days.

"We know every person who steps aboard one of our airplanes places their trust in us," Muilenburg said at a leadership forum in Dallas.

The Boeing team had made 96 flights totalling a little over 159 hours of air time with the updated software. Muilenburg said he joined one of the flights during which the crew performed different scenarios that exercised the software changes in multiple flight conditions.

"The software update functioned as designed," he said.

Last week Boeing cut its monthly 737 production by nearly 20 percent, signalling it did not expect aviation authorities to allow the plane back in the air anytime soon.

Chicago-based Boeing has not received any new orders for the 737 MAX since the crash in March, when deliveries also sank for the previously fast-selling aircraft.

The 737 MAX has been considered the likely narrowbody workhorse for global airlines for decades to come. There were more than 300 MAX jetliners in operation at the time of the Lion Air crash and about 4,600 more on order.

Muilenburg joined Boeing in 1985 and became CEO in July 2015 and chairman of the board in March 2016.