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 said last week that it had reprogrammed software on its 737 MAX passenger jet to prevent erroneous data from triggering an anti-stall system that is under mounting scrutiny.

Boeing said it will pay to train airline pilots on its 737 MAX aircraft.