The helicopter was on a mission Sunday to capture the country's most wanted militant when it crashed and burst into flames.
Twelve bodies were found Sunday, and military spokesman Maj. Gen. Tatang Sulaiman said the 13th victim, a first lieutenant, was found in the wreckage.
The Bell 412-EP helicopter was carrying 13 soldiers and crew when it went down about 35 minutes after taking off from Poso district's Watutau village, said Maj. Gen. Agus Surya Bakti, the regional military chief overseeing South and Central Sulawesi provinces.
It was not yet known what caused the 3-year-old helicopter to crash, though thunderstorms were thought to have played a part, Agus said.
More than 2,500 security forces, including elite army troops, have intensified their operations this year in Poso, a mountainous district of Central Sulawesi province considered an extremist hotbed, to try to capture Indonesia's most wanted militant, Abu Wardah Santoso. He leads the East Indonesia Mujahidin network, which has pledged allegiance to the Islamic State group.
At least five members of the network were killed by security forces this past week. Members of the group are thought to be hiding in Poso, where more than 1,000 people died in 2001 and 2002 in violence between Christians and Muslims.
Indonesia, a sprawling archipelago nation of about 250 million people, has been plagued by transportation accidents in recent years, including plane and train crashes and ferry sinkings.