A telegram from the National Search and Rescue Agency to the air force has requested assistance with the search.
While the aircraft is yet to take to Australian skies, Virgin Australia has 30 Boeing 737 MAX 8 planes on order, with the first of the fleet due to arrive in late 2019.
Privately owned budget carrier Lion Air was founded in 1999 and its only fatal accident to date was when a MD-82 crashed upon landing at Solo City in 2004, killing 25 of the 163 people on board, according to the Flight Safety Foundation's Aviation Safety Network.
The Boeing 737 Max 8 has been in commercial use since 2016.
Relatives of passengers of Lion Air flight that crashed into the sea, cry at Depati Amir airport in Pangkal Pinang, Indonesia, October 29, 2018.
Lion Air has confirmed that the aircraft had a "technical problem" on the previous flight, "which had been resolved according to the procedure".
He also shared a video he said had been taken from a tugboat off Karawang, just east of Jakarta, which appeared to show debris floating in the water.
The disaster is a setback for Indonesia's airline industry, which just emerged from decade long bans by the European Union and the U.S. over safety concerns.
Indonesian rescuers have found passengers' belongings and debris, but are yet to locate the main body of the plane. "We hope, we pray, but we can not confirm".
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Lion Air said that the aircraft was a passenger plane en route to a domestic location.
Data from FlightRadar24 shows the first sign of something amiss was around two minutes into the flight, when the plane had reached 2,000 feet.
The brand-new aircraft, which had at least 23 government officials on board, had sought to turn back just before losing contact, an air navigation spokesman told Reuters.
Items believed to belong to passengers have been found in the water, including ID cards and driver's licences, the search and rescue agency said on Twitter.
"The plane is so modern, it transmits data from the plane, and that we will review too".
Lion Air chief executive Edward Sirait said the Boeing jet had experienced a technical issue that required it to be briefly grounded for repairs.
The plane crashed shortly after taking off from an airport in Indonesia.
Lion Air, a low-priced airline, has been involved a number of incidents.
Indonesian airlines were barred in 2007 from flying to Europe because of safety concerns, though several were allowed to resume services in the following decade.