The National Disaster Mitigation Agency had said more than 680 people were stranded on Rinjani, an active volcano, based on figures from its entry gates where visitors are registered.
News portal Detik said two helicopters had been deployed to take the trekkers off the mountain and distribute food.
Sudiyono, who uses one name, said, "Information that we have from survivors is more than 500 people are trapped on the mountain and gathered near the volcano lake Segara Anakan".
Indonesian soldiers and a rescue team gather to prepare for evacuating tourists from Mount Rinjani.
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Agung Pramuja, an official of the West Nusa Tenggara Disaster Mitigation Agency, said the death toll from Sunday's quake stood at 16.
The Indonesian Red Crescent said it was dispatching hundreds of tarpaulins, blankets and hygiene kits to the affected areas as part of their initial response to the natural disaster.
The quake struck at 6:47am on Sunday when many people were still sleeping.
A 6.4 magnitude is strong enough to cause injuries and damage to buildings, but largely depends on how densely populated the affected area is.
There were reports it was also felt in Bali - 60 miles (100km) away - but there were no reports of damage there.
Indonesian President Joko Widodo flew to the island Monday to meet with the communities affected by the natural disaster as emergency aid began to be dispersed to the island.
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At least 14 people have died, and more than 160 were injured in the quake.
"Rinjani mountain climbing is closed temporarily because there is an indication of landslide around the mountain", Nugroho, said in a statement.
Some 200 people from 35 families whose house were damaged or destroyed had pitched tents there.
The quake struck at 6:47 a.m. on Sunday (2247 GMT on Saturday) and was only 4.35 miles deep (7 km), a shallow depth that would have amplified its effect.
Indonesia, one of the most disaster-prone nations on earth, straddles the so-called Pacific "Ring of Fire", where tectonic plates collide and a large portion of the world's volcanic eruptions and earthquakes occur.
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