According to the Detik news outlet, the minister confirmed that the Boeing 737-500, domestic flight SJY182, was carrying 53 passengers and 12 crew members in total when it took off from Jakarta.
Sumadi also confirmed that the crash site was near the island of Laki, part of the island chain dotting the north of Java.
Jakarta airport controllers lost contact with the plane at 14:40 local time (07:40 GMT) minutes after it had taken off.