There are fears the death toll will keep rising as rescuers step up the search of damaged or destroyed homes, schools and mosques.
At least 105 people were killed and 230 were injured in the magnitude 6.9 quake, which hit the tourist island of Lombok on Sunday night.
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Despite it being a popular tourist destination, no foreigners were recorded among the dead, BNPB spokesman Mr Nugroho told a news conference.
"Our hearts go out to the people affected by the quake".
Thousands of homes and buildings were damaged and those displaced camped wherever they could - in sports fields and on roadsides, cobbling together ramshackle shelters and building campfires for warmth.
A total of 8381 tourists, locals and workers of hotels and resorts on the three Gili islands - Gili Trawangan, Gili Air and Gili Meno - had been evacuated as of late afternoon on Tuesday, BNPB said.
A focus for rescuers is a mosque in Karang Pangsor village in North Lombok which collapsed with worshippers still inside. Many slept outside at night as they were afraid to go into their houses.
With not enough boats to evacuate tourists quickly and too few planes to fly them out of Lombok, many visitors were forced to wait for hours or camp on beaches and on the floor of the worldwide airport in Mataram.
Aid agencies including Oxfam, the Red Cross and Save the Children, working with local partner agencies, say they are scrambling to get sufficient aid to those most in need.
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The natural disaster hit the Indonesian island of Lombok, a popular tourist destination.
On Wednesday, rescuers retrieved the body of a woman from the rubble, but more victims are believed to be inside. "We saw everybody leaving in boats but no boat came to us", he told AFP. "Next time we will stay in France, or somewhere close", she said.
North Lombok is the hardest hit area.
National Disaster Mitigation Agency spokesman Sutopo Purwo Nugroho told The Associated Press that the damage was "massive" in northern Lombok, where the quake was centred, and that more than half the homes were destroyed or severely damaged.
Foreign tourists pull their suitcases as they walk past damaged buildings following a strong quake in Pemenang, North Lombok, Indonesia, Aug. 6, 2018.
As hopes of finding more survivors faded, a humanitarian crisis loomed for thousands left homeless and in desperate need of clean water, food, medicine and shelter.
It said it was not aware of any Irish casualties, but said there could be other Irish people who have not yet made contact.
"People were just throwing their suitcases on board and I had to struggle to get my husband on, because he was bleeding", she said.
Quakes continue to rattle the island, including a 5.5 magnitude tremor at around 2 a.m. (1800 GMT Monday), Indonesia's meteorology and geophysics agency said (BMKG).
Immigration authorities said that seven foreigners - from Belgium, Britain, Czech Republic, Denmark, France, South Korea and the United States - were injured in the quake and are being treated in hospital.