Dozens of aftershocks rippled through the area leading to falling debris and toppled concrete, which the country's disaster agency said caused most of the fatalities. He says several people have been injured.
A Malaysian tourist visiting the popular trekking destination of Mount Rinjani on Lombok was among those killed, according to East Lombok police M. Eka Fathurrahman.
The national park authority said on Monday that a key route to the peak of the 3,726-metre (12,224-foot) volcano had been cleared, and a helicopter was dropping supplies to others still picking their way to safety.
Mr Nugroho said the quake also triggered a large landslide from Mount Rinjani, a popular trekking destination.
Deputy Head of Mission Zamshari Sahaharan at the Malaysian Embassy in Jakarta said they were encouraging all Malaysian who knew tourists in Lombok to contact consular officials.
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"The quake killed at least 10 people, some 40 people are injured and dozens of houses were damaged", said Sutopo Purwo Nugroho, spokesman for Indonesia's disaster mitigation agency.
Hundreds of rescue workers are now working to evacuate them from Mount Rinjani, a popular hiking destination.
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.
A magnitude-6.4 natural disaster is considered strong and capable of causing severe damage.
The island was hit with a severe aftershock measuring 5.5 on the Richter scale 30 minutes after the first quake.
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Mr Pramuja said a landslide triggered by Sunday's quake trapped a group of six at the crater lake of Indonesia's second-highest volcano.
The jolt was felt about 100km away on the island of Bali, although there were no immediate reports of damage there.
"People are gathering on the streets and in empty fields to avoid collapsing buildings", he said.
The remains of Malaysian climber Siti Nur Ismawida Ismail, 30, who perished during the recent quake on the Indonesian island of Lombok, will be repatriated home tomorrow, according to news portal Astro Awani.
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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The quake was on land and did not trigger any waves or tsunami.