Both aircraft went through a series of rapid climbs and dives before crashing, killing everyone on board.
This led investigators to focus on the MCAS system, which automatically pushes the nose of a 737 Max down to offset a handling characteristic that causes the aircraft to pitch up, potentially causing it to lose lift and stall. In both crashes the MCAS systems activated, confusing the pilots on how to deal with it.
Boeing has been frantically working on a software fix to solve any issues with the system, such as reducing the MCAS's inputs to the flight controls and it no longer being triggered by a single sensor giving a wrong reading.
Safety regulators will review the fix once Boeing hands it over - a process that could take up to three months.
Muilenburg said 85pc of the 50-plus airlines flying the 737 Max had seen the updated software working in simulators.
He added that Boeing staff were "comprehensively testing the software to make sure that it does the job and they are taking the time to get it right. Safety is our responsibility, we own it and the work of the team will make the 737 Max one of the safest aeroplanes ever to fly".Worries about a wider issue with the 737 Max - for which Boeing has 5,000 orders worth about $600bn at list prices, making it the company's best-selling aircraft - have knocked $25bn off the value of Boeing.
Indonesian airliner Garuda has cancelled an order for 50 737 Max airliners in the wake of the crash, and other operators have threatened to take similar action.
Boeing has slowed down production of the 737 family of aircaft by a fifth to 42 a month but the planes are still building up at its plant in Renton, near Seattle.
Aviation consultancy IBA has calculated that each day a 737 Max is grounded costs its operator $150,000 as they face leasing replacement aircraft, passenger compensation and crew costs.
Airlines could try to claim back some of that cost from Boeing if the cause of the groundings is the company's fault.
The 737 Max could face further issues with reports that two airlines have started checking the aircraft's engines because of concerns about a problem that could cause them damage.
Bloomberg reported that a potential build-up of carbon around fuel nozzles in the CFM Leap-1B engines on a small proportion of 737 Maxs could damage the engines. American Airlines and Southwest, the two biggest operators of the aircraft, are now checking to see if this is an issue as a precautionary measure.
- Telegraph Media Group
