Muilenburg told the U.S. news outlet that Boeing is conducting simulated flights with air-safety regulators this week and hopes to obtain approval from federal aviation regulators by the end of the year for the resumed airline service of 737 Max airplanes.

Boeing CEO Dennis Muilenburg. [File photo: VCG]

Boeing 737 Max aircraft have been grounded across the world since March this year after initial probes showed that a fault in the flight control system was possibly behind two separate fatal air crashes in Indonesia and Ethiopia in October and in March, respectively. The two crashes killed all 346 people aboard.

Muilenburg did not specify when the U.S. top aircraft manufacturer would get a green light from the Federal Aviation Administration, but he disclosed that Boeing had completed a software update for the flight control system.

Announcing the completion of the software update on May 16, Boeing said it had also finished simulator testing and engineering test flight after the company flew the 737 Max with an improved flight control system for more than 360 hours on 207 flights.

Muilenburg said Boeing is working hard to win back the "damaged trust" of the general public who are worried about the air safety of 737 Max airplanes in the wake of the two air crashes.