Disaster Mitigation Agency spokesman Sutopo Purwo Nugroho said that nearly 400 foreign and local tourists had been registered since Sunday to climb the mountain, leaving from Sembalun monitoring post, about 11 kilometers (7 miles) from the crater.
"We are still searching for about 389 other tourists, mostly foreign tourists, to find out their condition and to evacuate them immediately," Nugroho said.
There have been no reports of injuries from the eruption.
The eruption interrupted flights for several hours at Ngurah Rai International Airport in Bali, about 135 kilometers (84 miles) from Lombok, and Selaparang airport in Mataram, the capital of West Nusa Tenggara province, located on Lombok Island.
Farms and trees around the 3,726-meter (12,224-feet) -high volcano were coated in a thin layer of gray ash, but nearby towns and villages were not in danger, Nugroho said.
Rinjani is among about 130 active volcanoes in Indonesia. The archipelago is prone to volcanic eruptions and earthquakes because of its location on the Pacific "Ring of Fire."
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