The pilot had reported technical difficulties after takeoff and asked for clearance to return to Addis Ababa.
That Senate investigation is one of several into the FAA and Boeing following two fatal MAX accidents since October.
Wicker's letter said the whistleblowers alleged that safety inspectors without proper safety training could have been participants on the Flight Standardization Board that evaluated the 737 MAX 8 to "determine the requirements for pilot type ratings, to develop minimum training recommendations, and to ensure initial flightcrew member competency".
At a news conference, Ethiopia's Minister of Transport Dagmawit Moges said the Ethiopian Airlines crew "performed all the procedures repeatedly provided by the manufacturer but was not able to control the aircraft".
It said air speed and altitude values on the left side of the 737 Max conflicted with data from the right sensor, causing flight control problems.
Families of the victims, regulators and travellers around the world have been waiting for signs of whether the two crashes are linked, and the extent to which Boeing technology and the actions of the Ethiopian Airlines pilots played a role.
The subpoenas stem from a criminal investigation that began after the Lion Air crash, sources said. A final investigation report typically isn't expected until up to a year after the crash.
They also requested records from Peter Lemme, who worked for Boeing as a flight controls engineer from 1981 to 1997, long before the MAX was in development. They also recommended that aviation officials verify that issues have been adequately addressed before allowing the planes to fly again.
The nose-down commands were issued by Boeing's so-called MCAS software.
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And those lower clubs know they will need pretty much two matches against the giants of the Premier League to score just one goal. It has taken him so far quite a number of games to nearly trust his own body not to surrender again.
That's significant because the sensor is suspected of sending faulty signals to a flight control system created to force the nose of the plane down to prevent a stall. "We will submit the update for FAA (Federal Aviation Administration) review once that work has been completed in the coming weeks".
Despite the conciliatory comments in the wake of suggestions of tension between United States and Ethiopian investigators, the way in which the Ethiopians presented what is an internationally significant report is likely to raise questions about the processes involved.
The Ethiopian Airlines flight was headed to Nairobi on a clear morning on March 10 when it plummeted nose-first into a field outside Addis Ababa just minutes after take-off, having reportedly experienced erratic steep climbs and descents.
Ethiopian Airlines said its crew had followed all the correct guidance to handle a hard emergency.
Boeing is now developing a software fix for MCAS that it says will add inputs from a second AOA sensor and an indicator light that will alert pilots when something is wrong. Boeing's procedures instruct pilots to leave the MCAS disconnected and continue flying manually for the rest of the flight.
Most accidents take months of analysis because of the need to trace backwards to find a root cause from tangled evidence.
"We don't have any reservations from different stakeholders who were engaged in the investigations", chief investigator Amdye Ayalew Fanta said.
The press conference in Ethiopia.
"All in all, the major objective of this investigation is to make sure that there is safety in the aviation sector", she said.
Ethiopian officials have announced the pilots of a doomed Boeing 737 Max airliner followed the manufacturer's instructions on turning off an anti-stall system that can force the plane's nose down, but could not regain control of the aircraft before last month's deadly crash.