Boeing's chief executive Dennis Muilenburg, grappling with the worst crisis of his tenure, said the company is taking action to "fully ensure" the safety of its 737 Max plane following two deadly crashes amid heightened scrutiny of the programme's development. The world's biggest plane maker will "soon" upgrade a software and related pilot training programme it has developed in the wake of Indonesia's Lion Air crash in October, Mr Muilenburg said on Monday, in a letter addressed to airlines, passengers and the aviation community. "We know lives depend on the work we do," Mr Muilenburg said. "Together, we’ll keep working to earn and keep the trust people have placed in Boeing." The flight-data recorders of Ethiopian Airlines flight 302 that crashed in Addis Ababa more than a week ago revealed "clear similarities" between the 737 Max jet and the Lion Air plane of the same model that plunged into the Java sea killing all 189 people on board, Ethiopian officials said. "Based on facts from the Lion Air Flight 610 accident and emerging data as it becomes available from the Ethiopian Airlines Flight 302 accident, we’re taking actions to fully ensure the safety of the 737 Max," Mr Muilenburg said. "We also understand and regret the challenges for our customers and the flying public caused by the fleet’s grounding." Boeing is working in co-operation with the US Federal Aviation Administration, the Department of Transportation and the National Transportation Safety Board on all issues relating to both the Lion Air and the Ethiopian Airlines accidents, the executive said. Mr Muilenburg said work is progressing "thoroughly and rapidly" to learn more about the Ethiopian Airlines accident and understand the information from the aircraft's cockpit voice and flight-data recorders. The executive's comments came after reports of heightened scrutiny by regulators and prosecutors into whether the safety approval process of the 737 Max was flawed. Boeing shares fell 1.8 per cent to $372 at end of trading in New York on Monday. After similarities arose between the Ethiopian Airlines and Lion Air crashes, regulators around the world grounded the 737 Max jets and Boeing temporarily halted deliveries of its best-selling aircraft. The delivery delays, pending the investigation, could cost Boeing about $400m a month in cash flow loss in addition to compensation fees, according to Bloomberg Intelligence. The Max 8 make was intended to be the future industry workhorse.