Rescue teams have yet to reach Nagekeo, the region closest to the epicentre, after landslides blocked roads and disrupted communications, officials said.
"The quake was massive, the shock was so strong," said Nona, a 51-year-old resident of Talibura, a village in East Nusa Tenggara.
"There were 13 of us inside the house and we all ran to save ourselves."
Tsunami waves of less than one metre were recorded in several parts of the Southeast Asian nation after the early morning quake. Authorities lifted a tsunami warning about three hours later.
Earlier, rescuers in the port town of Maumere found 20 dead, six injured and two people trapped under rubble, said Fathur Rahman, head of the city's rescue agency. Maumere is the main town in Sikka Regency on Flores Island in eastern Indonesia.
Suharyanto, head of the National Disaster Mitigation Agency, said residents remained trapped in several buildings across the affected area, while there were reports of landslides blocking several roads.
Teams have yet to reach Nagekeo and mobile communications in the region were affected, Fathur told Reuters earlier.
Attempts to reach the area by road were thwarted by landslides, while another team was trying to reach it by ferry, he said.
About 2000 residents in Nagekeo evacuated, and damage was reported to homes, warehouses and government buildings, the National Disaster Mitigation Agency said.
Authorities also reported power outages and traffic congestion in parts of the regency.
East Nusa Tenggara Governor Emanuel Melkiades Laka Lena told a press conference that at least five people were killed when buildings collapsed as they slept.
Preliminary data showed 157 homes were heavily damaged, 41 moderately damaged and 148 lightly damaged.
Damage was also reported at 87 schools, 18 health facilities, five places of worship and six office buildings, along with other infrastructure.
Parts of a building collapsed into dust and rubble as people screamed and ran in the street, according to a Facebook video, verified by Reuters as being filmed at a port in Maumere.
Rescuers were searching for survivors beneath a partially collapsed port building.
Siti Sulfia Bira, 37, who lives with her family near the port in Maumere, said she rushed to higher ground when the tremors started.
"At the moment we don't dare to go home just yet because the situation isn't stable; we still worry that there might be more tremors coming," she told Reuters.
Strong shaking was felt across East Nusa Tenggara, West Nusa Tenggara and parts of South Sulawesi, with residents in several areas reporting tremors lasting about a minute.
"Most of the people felt the shock and scattered out of their homes," the agency said.
A hospital in Ende district in East Nusa Tenggara was moving patients outside, Kompas TV footage showed, while Kompas.com reported at least one landslide.
Indonesian geophysics agency recorded the first quake at a depth of 15km, followed by several aftershocks.
The agency said the same area was hit by a magnitude 7.5 earthquake in 1992 that caused extensive destruction.
Australia's tsunami warning centre said the undersea quake posed "no tsunami threat to the Australian mainland, islands or territories".
Indonesia straddles the Pacific Ring of Fire, a seismically active zone where tectonic plates meet, triggering frequent earthquakes and volcanic eruptions.
In 2018, a magnitude 7.5 earthquake and tsunami struck the city of Palu on Sulawesi island, killing more than 4000 people.
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