"In their rucksacks we found cooking equipment but no food, so we think they ran out of food in very cold weather,'' Martadin told state news agency Antara.
The exact cause of death has not been established but the 3,726-meter peak has seen bad weather in recent days, Police Sergeant Eko told reporters.
It takes at least three days to hike to the crater of Mount Rinjani, Indonesia's third highest volcano.
It last erupted in 2004 but is still classified as an active volcano, and with 150 in total, Indonesia has the highest number of active volcanoes in the world.