The Lion Air plane took off from Jakarta's Soekarno Hatta airport at 6.20am and lost contact with air traffic control about 13 minutes later as it crashed into the sea off Tanjung Karawang, about 70 kilometres east of Jakarta.
Few details have been released but the ministry said it had looked over half a dozen jets so far and discovered that one had a problem linked to its cockpit display while another had a glitch in a jet stabilisation system.
Indonesia is one of the world's fastest-growing aviation markets but its safety record has been patchy.
Its transport safety panel investigated 137 serious aviation incidents from 2012 to 2017.
"There is a lot of little debris, plane wheels, and seats - all totally destroyed and in pieces", said Isswarto, commander of the Indonesian navy's search-and-rescue division. "Passengers' safety must be made a priority".
Divers believe they have detected a signal that may be from the cockpit voice recorder and they believe they have found what they have always been looking for - the plane's fuselage.
Divers have also been scouring the seabed for the cockpit voice recorder after a "low ping signal" was detected by a sonar locator.
All 189 passengers and crew aboard a crashed Indonesian Lion Air jet were "likely" killed in the accident, the search and rescue agency said on 29 October, as it announced it had found human remains.
Syachrul Anto was part of a diving team searching for body parts from the ill-fated jet, which crashed into the Java Sea on Monday.
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Operational Director Bambang Suryo Aji on Monday ruled out the possibility that the plane exploded in the sky as there has been no burnt signs on the debris and body parts found floating around the crash site.
Lion Air has claimed a technical problem was fixed after the Bali fight.
In global air transport, Lion Air was among six airlines of several countries that fly the new Boeing 737 model.
Data from flight-tracking websites show both flights had highly erratic speed and altitude after takeoff, though confirmation is required from data recorded by the aircraft's "black box" flight recorders.
But the devices in recent decades have been computerized and rely on memory chips that have proven highly reliable. Investigators have said it was damaged and requires special handling to retrieve its data.
"That was a pretty hard hit", he said.
The Lion Air tragedy has raised fresh questions about the safety record of a country whose airlines were for years judged too unsafe to fly over Europe.
"From here we will analyse what happened to that flight", Nurcahyo Utomo, head of Indonesia's transportation safety committee, told reporters.