By late afternoon, more than 250 people had reached a relief post in Sembalun village and a team of rescuers has reached hundreds more near the mountain's crater lake, a local military official, Arifianto, told Indonesian TV.
The 6.4-magnitude quake in Lombok, which was adjacent to Bali, has killed 17 people, including the Malaysian female tourist and a domestic tourist, Indonesia's national Disaster Mitigation Agency (BNPB) said.
Miss Coulson's aunt Victoria Toas said: 'They actually believed the volcano was erupting until they spoke to us and we told them it was an natural disaster.
"I got out of my bed and then I saw a landslide (with) rocks falling down".
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.
At least 162 people were left injured following the tremor, 94 severely according to the Indonesian Red Crescent.More news: Elliott holds off Truex at Watkins Glen
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"I felt the earth move. and thought 'Huh?" The guides were screaming, 'Don't die, don't die.' One of the guides had to shake me and take me by the hand.
A magnitude 6.4 natural disaster is considered strong and is capable of causing severe damage.
Anna Stevens and Kathryn Coulson, both 21 from Darlington, County Durham, were on a trekking tour on Mount Rinjani when the 6.4-magnitude quake struck Sunday.
There have been more than 270 aftershocks after the initial powerful quake.
Indonesia is particularly prone to seismic activity due to its location along the Pacific's "Ring of Fire", a chain of volcanoes and fault lines.
This story has not been edited by Firstpost staff and is generated by auto-feed.