At least 14 people have died, and more than 160 were injured.
The National Disaster Mitigation Agency said more than 680 people are stranded on Rinjani based on figures from its entry gates where visitors are registered.
Hikers were able to start descending the mountain Monday after guides discovered an alternate route that was unaffected by the landslides.
Hundreds of other hikers managed to get off the mountain on Sunday, according to officials.
Ali bin Dachlan has also issued a seven-day emergency as his regency was the worst-hit by the shallow magnitude 6.4 quake.
"There are now six people left".
One of the two bodies recovered by rescuers yesterday was that of climber Muhammad Ainul Muksin, 26, who died in a landslide during the quake.
"I mobilized 142 Kopassus soldiers this morning to help the tourists that are stuck on Mount Rinjani", said Indonesian Military commander Air Marshal Hadi Tjahjanto at the Jakarta Police headquarters today.
Thousands of buildings were destroyed across Lombok, including a health clinic.
Malaysian tourist Siti was reportedly found dead, crushed by a collapsed wall, at that location.
The 3,726 metre-tall (12,224 feet) Rinjani is the second-highest volcano in Indonesia and a favourite among sightseers.
A total of 7,593 people are staying in temporary shelters, according to officials.
The West Nusa Tenggara administration has declared a seven-day state of emergency following a magnitude 6.4 quake that rocked Lombok Island and claimed at least 17 lives on Sunday.
The initial tremor was followed by two strong secondary quakes and more than 100 aftershocks.
Indonesia is prone to quake as it lies on vulnerable quake-affected areas called the Pacific Ring of Fire.