190417 Boeing
workers are pictured next to a Boeing 737 MAX 9 airplane on the tarmac at the Boeing Renton Factory in Renton, Washington. Image Credit: AFP

Boeing Co is making "steady progress" on the path to certifying a software update to the grounded 737 Max and has made the final test flight before a certification flight, its chief executive said on Wednesday.

Boeing's newest 737 model, the Max, was grounded worldwide in March following two fatal crashes, one on Lion Air in Indonesia in October and another on Ethiopian Airlines in March, which together killed all 346 on board.

Battling its biggest crisis in years, the world's largest aircraft manufacturer is under pressure to convince Max operators and global regulators that the aircraft can be safely recertified to fly again.

"We are making steady progress toward certification," Boeing CEO Dennis Muilenburg said in a video on his Twitter account.

Standing in front of a 737 Max plane at Boeing Field in Seattle, Muilenburg said the company had completed on Tuesday the official engineering flight test with the updated software with technical and engineering leaders on board the airplane.

"That was the final test flight prior to the certification flight," he said.

Muilenburg said he had seen first-hand the new software in its final form operating in a range of flight conditions, adding that his team was committed to making the 737 Max "one of the safest airplanes ever to fly."

Of some 50 Max customers and operators, Muilenburg said more than 85 per cent had experienced the new software in simulator sessions and that there had been 120 737 Max test flights held with more than 230 hours of air time with the new software.

Boeing shares, which have lost about 11 per cent of their value since the March 10 Ethiopian crash, ended 1.1 percent lower at $377.52 on Wednesday.