The Indonesian rescue agency has been carrying out search operation since the crash and over 300 people, including soldiers, police and local fishermen have been pressed into action.
The jet was a Boeing 737 MAX 8, which can carry up to 200 passengers.
Lion Air Group's Chief Executive Edward Sirait earlier told Reuters: "We can not give any comment at this moment".
Lion Air, one of Indonesia's youngest and biggest airlines, said the brand-new aircraft, on a 1-hour-and-10-minute flight to Pangkal Pinang on an island chain off Sumatra, was carrying 181 passengers, including one child and two babies, and eight crew members.
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However, the 89-run grand total seems quite promising after the lost 6 wickets in just 22 runs at the beginning of the game. It was like a vehicle crash in slow motion", Finch told reporters after his side crumbled at Sheikh Zayed Cricket Stadium.
Lion Air said in a statement that the pilot and co-pilot were experienced, with more than 11,000 flight hours between them.
The disaster is a setback for Indonesia's airline industry, which just emerged from decade long bans by the European Union and the United States over safety concerns.
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The pilot had asked to return to Jakarta's Soekarno-Hatta airport, the head of Pangkal Pinang's search and rescue office, Danang Priandoko, told local news outlet Kompas.
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They said the "hypotheses" proposed so far in the Saudi investigation need to be backed by facts to be considered credible. She also reiterated the federal government's call for a thorough investigation in collaboration with Turkish officials.
Lion Air is a budget carrier and has been involved in a number of incidents. Data for Flight 610 on aircraft tracking website FlightAware ends just a few minutes following takeoff.
"When we arrived at the location, we found aircraft debris, a buoy, cellphones, and several objects", said Air Marshal Syaugi at a joint press conference on Monday morning with Indonesia's national transportation safety committee KNKT. "We're confused. We hope that our family is still alive", she said. Plane seats were also sighted among the debris.
Items believed to belong to passengers were found in the water including ID cards and driver's licences, Indonesia's search and rescue agency Basarnas said. The airline reportedly said there was a technical issue with the same aircraft on its previous flight, although it indicated this had been resolved.
Lion Air is considered one of Indonesia's fastest growing and most affordable airlines.
In 2013, Lion Air flight 904 crashed into the sea on landing at Bali's Ngurah Rai International Airport.
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Florida gubernatorial candidate Andrew Gillum says that anytime a police officer pulls out a weapon, they have gone "too far". It's unknown if these new revelations will have an impact on the Governor's race. "Everyone will get a fair shake".
"It's true that Lion Air JT 610 has lost contact".