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.
"On behalf of the people of Singapore, I offer my heartfelt condolences to Indonesia and the families affected by the disaster", said PM Lee in his letter. Among the fatalities were a 30-year-old Malaysian climber and another hiker who was hit by a landslide, local media reported.
A total of 189 foreign tourists were among the hikers rescued by a joint-force of Indonesian special military force unit, police and rescuers, Sutopo said.
The jolt was felt some 100 km (60 miles) away on the bustling resort island of Bali, although there were no reports of damage there.
Hiking trails on the mountain were closed following the quake due to fear of further landslides.
Among the procedures applied for the affected foreign tourists was to waive the hotel charges for the next day after Sunday's strong quake, which hit the popular destination island located in West Nusa Tenggara province, said the minister.
Some 160 people were injured as a result, said Mohammad Rum, head of West Nusa Tenggara disaster agency.
Those whose homes were "lightly damaged" will receive 10 million rupiah, with the funds expected to be disbursed within the next 50 days.
The death toll from a magnitude-6.4 quake in Indonesia's Lombok Island rose to 16 on the evening of July 29.
The 6.4 magnitude quake brought with it several aftershocks, after which tonnes of rocks and mud rained down the mountain blocking all the hiking routes.
The search will be halted at sunset, search and rescue officials said.
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