Two critically-endangered Sumatran elephants have been found dead in Indonesia's Aceh province with their tusks missing, police said Monday.

The first was found in a palm oil plantation in East Aceh district on Sunday, while the other was discovered in Aceh Jaya district on Friday, Aceh police spokesman Gustav Leo told AFP.

"Officials are still on the way to retrieve the carcass in the latest case," he said.

"But officials have examined the elephant found on Friday and found traces of poison in its faeces," he added.

"We suspect poachers could have poisoned the elephants' food and then wait(ed) for them to die before removing the tusks," he said.

The animals are usually either killed by villagers, who regard the beasts as pests that destroy their plantations, or by poachers for their tusks.

There are fewer than 3,000 Sumatran elephants remaining in the wild, according to the International Union for Conservation of Nature, marking a 50 percent drop in numbers since 1985.

Conflicts between humans and animals are increasing as people encroach on wildlife habitats in Indonesia, an archipelago with some of the world's largest remaining tropical forests.