The pilot "was given clearance" to return to Addis, chief executive officer Tewolde GebreMariam told journalists in the Ethiopian capital when asked whether there had been a distress call.
The new Boeing 737 MAX: Two crashes in six months
The 737 MAX, a new plane from US aircraft manufacturer Boeing, faces fresh scrutiny of its safety record after being involved in two crashes in six months.
The single-aisle airliner, which undertook its first commercial flight in May 2017, came under the spotlight in October last year in the wake of a fatal accident in Indonesia.
Lion Air Flight 610 vanished from radar shortly after taking off from Jakarta on October 29, crashing into waters off the north coast of Java Island and killing all 189 people onboard.
About 30 relatives of the crash victims have since filed lawsuits in the United States against Boeing, alleging that faults with the new airliner, including with its anti-stalling system, led to the deaths.
Questions were raised by experts and a pilots' union in the US about whether pilots had been properly trained and whether Boeing had fully shared data about changes made to the on-board control systems.
Boeing responded by saying that the 737 MAX was "as safe as any airplane that has ever flown the skies."
There is no indication that a technical problem was to blame for the crash of the Boeing 737-800 MAX operated by Ethiopian Airlines on Sunday which crashed minutes after taking off from Addis Ababa bound for Nairobi.
An investigation by aviation experts and analysis of the blackbox flight recorders is expected to shed light on the causes of the crash.
Boeing is struggling to keep up with demand for the new aircraft, which offers far better fuel efficiency than earlier versions of the 737, the world's top-selling airliner.
Around 350 planes have been delivered to customers, with another 5,011 orders taken by Boeing, according to figures at the end of January.
Component suppliers and particularly the manufacturer of its engines -- CFM, a joint venture between US-based General Electric and France's Safran -- have struggled to keep up with demand.
Forced to announce delays in deliveries to clients, Boeing has sent some of its own employees to work alongside CFM workers with the aim of increasing production from its current rate of 52 planes a month to 57.
The 737 MAX family of planes includes versions with different seating capacities, with a maximum 230 for the MAX 9.
The price per plane ranges from 99.7-129 million dollars (89-117 million euros), though discounts are usually given to clients for large orders.
Its main competitor is the Airbus A320, which is also designed for short and medium-haul flights.