"As of this morning, we've received two (body) bags, one with passenger belongings and the other with body parts," Jakarta police spokesman Yusri Yunus told Metro TV.
Also Read|Indonesian Aircraft, With 62 Passengers Onboard, Feared To Have Crashed - All We Know So Far
Indonesian authorities also say they have found the location where they believe a Boeing 737 passenger plane crashed into the sea.
More than 10 ships were deployed to the site with navy divers.
Investigators are analysing items they believe to be wreckage.
Search and rescue efforts were suspended overnight but have resumed early on Sunday.
What happened to the aircraft?
The Sriwijaya Air passenger plane departed Jakarta airport at 14:36 local time (07:36 GMT) on Saturday.
Minutes later, at 14:40, the last contact with the plane was recorded, with the call sign SJY182, according to the transport ministry.
The usual flight time to Pontianak, in the west of the island of Borneo, is 90 minutes.
The aircraft did not send a distress signal, according to the head of national search and rescue agency Air Marshal Bagus Puruhito.
It is thought to have dropped more than 3,000m (10,000ft) in less than a minute, according to flight tracking website Flightradar24.com.
Witnesses said they had seen and heard at least one explosion.
Who was on board the flight?
There were thought to be 50 passengers - including seven children and three babies - and 12 crew on board, though the plane has a capacity of 130. Everyone on board was Indonesian, officials say.
Relatives of the passengers have been waiting anxiously at the airport in Pontianak, as well as at Jakarta's Soekarno-Hatta International Airport according to BBC.
What do we know about the plane?
According to registration details, the plane was a 26-year-old Boeing 737-500.
It was in good condition, Sriwijaya Air chief executive Jefferson Irwin Jauwena told reporters. Take-off had been delayed for 30 minutes due to heavy rain, he said.
Sriwijaya Air, founded in 2003, is a local budget airline that flies to Indonesian and other South-East Asian destinations.
The plane went missing about 20km (12 miles) north of the capital Jakarta, not far from where another flight crashed in October 2018. A total of 189 died when an Indonesian Lion Air flight plunged into the sea about 12 minutes after take-off from the city. That disaster was blamed on a series of failures in the plane's design but also faults by the airline and the pilots. It was one of two crashes that led regulators to pull the Boeing 737 Max from service. The model resumed passenger flights in December after a systems overhaul.