The Boeing 737 was orginally scheduled to arrive at Pangkal Pinang at 7.20am.
Lion Air chief executive Edward Sirait said the Boeing jet had experienced a technical issue that required it to be briefly grounded for repairs.
Syaugi said the search and rescue teams had come from Jakarta, Bandung and Lampung and were headed to Tanjung Karawang, where the plane is believed to have gone down.
"We need to find the main wreckage", Bambang Suryo, operational director of the agency, told reporters.
Lion Air said in a statement that the plane's pilot-in-command had logged more than 6,000 flight hours before the incident, while the co-pilot had logged more than 5,000 flight hours.
At the same news conference, a Lion Air official said there were two foreigners on board the plane: its pilot, originally from New Delhi, and an Italian citizen.
Indonesian officials quoted by Channel News Asia said Lion Air had taken delivery of the brand new Boeing 737-800 MAX, described as "an updated, more fuel-efficient version of the manufacturer's workhorse singe-aisle jet" on August 13 of this year.
The crash is reportedly the first involving the widely sold 737 Max, an updated and more efficient version of the single-aisle jet.
According to the BBC, the plane's pilots had requested to return to the airport, the head of Pangkal Pinang's search and rescue office, Danang Priandoko, told local news outlet Kompas.
The aircraft was reported to be a Boeing 737 MAX 8, a model only in commercial use since 2016.
The plane took off from Jakarta airport and crashed 13 minutes later.
"Lion Air aircraft debris JT 610 falling in the waters of Karachi".
It was not immediately clear how many people were on board. Experts will be seeking to recover the plane's black boxes: the cockpit voice recorder and data flight recorder.
"A few flakes of Lion Air plane that crashed in waters of Karachi", he wrote in the first tweet, accompanying the photos.
Jakarta-based Lion Air, owned by privately held PT Lion Mentari Airlines, is a budget carrier that started operations in 2000.
As per Indonesia's finance ministry spokesman Nufransa Wira Sakti there were 20 officials on board the crashed Lion passenger jet. The transport ministry said crisis centres have been set up Pangkal Pinang's airport and Jakarta's Soekarno-Hatta airport.