Sutopo Purwo Nugroho, spokesman for Indonesia's disaster mitigation agency, said on Twitter late Sunday that out of 820 people who were on the slopes of the volcano when the quake struck, 246 had been successfully evacuated.
He said 617 of those trekking at the time were foreigners.
Two trails were impassable following the earthquake, he said.
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The news portal Detik reported that two helicopters had been deployed to take the trekkers off the mountain and distribute food.
Agung Pramuja, an official of the West Nusa Tenggara Disaster Mitigation Agency, said the death toll from Sunday's earthquake stood at 16.
Asdiyanto, an official at the North Lombok Disaster Mitigation Agency, said: "The latest information from the team in the field is that today all the families stuck on Mount Rinjani will be evacuated via the Sembalun trail.
"This is being handled by the management team from Mount Rinjani National Park," said Asdiyanto, who, like many Indonesians, uses one name.
A magnitude-6.4 earthquake is considered strong and capable of causing severe damage.
The Lombok quake, which struck at 6:47 a.m. (8:47 p.m. ET Saturday), was only 4.35 miles deep, a shallow depth that would have amplified its effect.
It was centered 30 miles northeast of the city of Mataram, according to the U.S. Geological Survey, but it was also felt strongly to the west on the neighboring island of Bali, Indonesia’s top tourist destination.
Earthquakes are common in Indonesia, which is on the seismically active"“Ring of Fire" on the rim of the Pacific Ocean.