Debris thought to be from the plane, including aircraft seats, was found near an offshore refining facility in the Java Sea, an official of state energy firm Pertamina said.
The effort to find the wreckage and retrieve the black boxes represents a major challenge for investigators in Indonesia, where an AirAsia Airbus jet crashed in the Java Sea in 2015. Flight QZ8501 was on en route from Surabaya to Singapore when it crashed on Dec 28, 2015.
Under international rules, the US National Transporation Safety Board will automatically assist with the inquiry into Monday's crash, backed up by technical advisers from Boeing and US-French engine maker CFM International, co-owned by General Electric and Safran.
The accident is the first to be reported involving the widely sold Boeing 737 MAX, an updated, more fuel-efficient version of the manufacturer's workhorse single-aisle jet.
US-based Boeing said it was "deeply saddened" by news of the crash.
"We express our concern for those on board, and extend heartfelt sympathies to their families and loved ones," it said in a statement.
"Boeing stands ready to provide technical assistance to the accident investigation."
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