Rescue agency spokesman Sutopo Purwo Nugroho posted photos on Twitter of debris that included a crushed smartphone, books, bags and parts of the aircraft's fuselage that had been collected by search and rescue vessels that converged on the area.
A telegram from the agency to the Indonesian Air Force requested assistance with the search in waters off West Java. Divers have been trying to locate the plane's wreckage.
Suyadi, a marine transportation officer in Tanjung Priok, North Jakarta, told The Jakarta Post he received a report at 6:45 am from a tugboat that its crew had seen a downed plane, suspected to be the Lion Air jet, at Tanjung Bungin in Karawang, West Java.
"At 7:15 am, the tugboat reported it had approached the site and that the crew had seen debris from a plane," Suyadi said.
A tanker and a cargo ship approached the area, he said, and a rescue boat from the agency was also on its way.
Debris, thought to be from the plane, including seats, was found near an offshore refining facility in the Java Sea, an official with state energy firm Pertamina said.
The plane was scheduled to land at Depati Amir Airport in Pangkal Pinang at 7:10 am.
There were two pilots and six flight attendants on board, the National Transportation Safety Commission said in a statement.
Sindu Rahayu, from the Indonesian Air Transportation Directorate General, said in a statement: "The directorate general is coordinating with the National Search and Rescue Agency, Lion Air, the Sea Transportation Directorate General and the Indonesian Flight Navigation Service Institution in search and rescue activities."
The aircraft was delivered to Lion Air in August. It was powered by two CFM LEAP-1B engines.
Flightradar24 tweeted that the plane was "brand new" and Lion Air received it only three months ago.
Australia told Indonesia that it had not received any emergency signals from the plane, rescue agency chief Syaugi said.
After the crash, the Australian government instructed its officials and contractors not to fly on Lion Air. It made the announcement on its website. The crash is Indonesia's worst air disaster since an Air-Asia flight from Surabaya to Singapore plunged into the sea in December 2014, killing all 162 on board.
Monday's flight also appears to have crashed in the Java Sea. The search and rescue agency said the plane ended up in waters 30 to 35 meters deep. Oil slicks could be seen around the area where contact was lost with the aircraft.
Preliminary flight tracking data from Flightradar24 show the aircraft climbed to about 1,524 meters before losing height, then regaining it, before finally falling toward the sea.
It was last recorded at 1,112 meters and its speed had risen to 638 km/h, according to data obtained by the tracking website, which could not immediately be confirmed.
The plane's last recorded position was about 15 kilometers north of the Indonesian coast, according to a Google Maps reference of the last coordinates reported by Flightradar24.
The accident is the first one reported of a Boeing 737 MAX, an updated, more fuel-efficient version of the manufacturer's workhorse single-aisle jet. The new planes began operating last year.
The first global delivery went to Lion Air's Malaysian subsidiary, Malindo Air.
Lion Air chief executive Edward Sirait said the plane involved in Monday's crash had experienced a "technical problem" on a previous flight.
He said this had been resolved "according to procedure" following a flight from Denpasar to Cengkareng, but he did not specify what the problem was.
Founded in 1999, Lion Air's only fatal accident was in 2004, when an MD-82 crashed on landing at Solo City, killing 25 of the 163 people on board, the Flight Safety Foundation's Aviation Safety Network said.
However, six other Lion Air jets, including one that crashlanded in waters short of the runway on the Indonesian resort island of Bali in 2013, were damaged beyond repair in various accidents, according to the Aviation Safety Network website. There were no fatalities among the 108 people on board the Bali flight.
Lion Air was removed from the European Union's air safety blacklist in June 2016.
In April, the privately owned airline announced it would buy 50 Boeing 737 MAX 10 narrow-body jets at a total cost of $6.24 billion. Lion Air is one of the US planemaker's largest customers globally.
Indonesian TV showed footage of dozens of people waiting anxiously outside Pangkal Pinang airport while officials brought out plastic chairs.
