Edward Sirait, the president of Lion Air, has said the company was aware of reports of problems on the flight on Sunday and that a technical issue was "resolved in accordance with the procedures released by the plane manufacturer".
Search teams are using an underwater drone, as well as underwater "pinger locators", to try to pick up the sonar signals from the cockpit recorders.
"We strongly believe that we have found a part of the fuselage of JT610", military chief Hadi Tjahjanto reportedly told told TV One.
Its contents may help explain why the almost brand new Boeing 737 MAX 8 went down.
Boeing officials are expected to meet with Lion Air on Wednesday, after Indonesia ordered an inspection of the United States plane maker's 737-MAX jets.
"The bigger picture here is that you've got a lot of American carriers flying the same aircraft", Stephen Wright, aviation expert at the University of Leeds, told AFP.
According to the engineers, the aircraft's tech log shows a record of a problem with "elevator feel and control" on the last flight the day before the tragedy that claimed 189.
The accident has also resurrected concerns about Indonesia's patchy air safety record which led to a now-lifted ban on its planes entering USA and European airspace.
On Wednesday, Indonesia's navy said a 22-metre object had been found at a depth of 32 metres.
In a 2015 interview, Kirana said that "my airline is the worst in the world, but you don't have a choice".
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Ground staff lost touch with flight JT610 of Indonesian budget airline Lion Air 13 minutes after the Boeing 737 MAX 8 took off early on Monday from Jakarta, on its way to the tin-mining town of Pangkal Pinang.
Indonesia's transport minister ordered an inspection of all 737-MAX aircraft on Tuesday.
An Indonesian Transportation Ministry Official, Captain Avirianto, said Lion Air had 11 of the new-era models while Garuda had one.
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 single-aisle jet.
But the narrow-body jet was subsequently cleared for commercial delivery and has had thousands of orders from more than 100 customers worldwide.
Meanwhile, Indonesian search and rescue officials have begun recovering body parts from the scene of the crash, in addition to ID cards, bags, mangled mobile phones and other belongings.
Authorities have all but ruled out finding any survivors, with 49 body bags containing human remains so far sent for identification.
The pair were later identified as Ine Yunita Savitri and her husband Wahjoe Noegrohantoro, who was on the downed jet.
"I keep praying for a miracle, although, logically, the plane has sunk in the ocean", Toni Priyono Adhi, whose daughter was aboard, said.