The development of Boeing's 737 MAX jets is reportedly being investigated by US prosecutors and the country's department of transport.The MAX 8 and MAX 9 have been grounded worldwide after two fatal crashes in under five months, the most recent last week when 157 people died when an Ethiopian Airlines jet came down.Reuters news agency said it had been told about the investigation by two people briefed on the matter.It said the US justice department was investigating how Boeing was regulated by the US airline authority, the Federal Aviation Administration (FAA).The department of transport is also said to be looking at the FAA's oversight of the plane-maker, as well as its development of the 737 MAX.Image:The Ethiopian plane's 'black boxes' were sent to France for analysisA subpoena has already been sent to someone involved in the aircraft's development, requesting emails and other communications, a source told Associated Press.It comes as Boeing's boss released an open letter saying the company will soon release a software update for the plane and offer updated pilot training.Dennis Muilenburg said his company was helping crash investigators in Ethiopia and that he realises "lives depend on the work we do".Numerous countries and airlines temporarily pulled the plug on the aircraft after the Ethiopia crash, with Boeing eventually giving in and issuing a worldwide grounding.Ethiopia's transport minister said on Monday there was a "clear similarity"between the Ethiopian Airlines crash and October's Lion Air crash that killed 189 people off Indonesia.Image:Mourners of victims of the Ethiopian Airlines flightDagmawit Moges cited preliminary data retrieved from the flight data recorder of the Ethiopian Airlines plane.The FAA also says satellite tracking data shows Flight ET302 made similar manoeuvres to those of Lion Air Flight 610.Both jets flew with erratic altitude changes that could indicate the pilots struggled to bring the aircraft under control.A problem with the flight-control software is suspected of playing a role in the crashes.Image:The Lion Air crash killed 189 people in October 2018The system is designed to point the nose down to regain stability when it thinks a stall is imminent, but a report into the Lion Air crash found there was an "erroneous" input from one of the sensors that measures the plane's angle.Airlines around the world are closely watching Boeing's response - the US firm is understood to have an order backlog of more than 4,000 for the MAX.