At least 200 bodies were found in one coastal city and the toll was expected to be far higher.
The quake on Wednesday started fires, severed roads and cut off power and communications to Padang, a coastal city of 900,000 on Sumatra island. Thousands fled in panic, fearing a tsunami.
It was felt hundreds of kilometres away in Malaysia and Singapore, causing buildings there to sway.
The undersea quake of 7.6 magnitude was followed by a powerful, shallow inland earthquake on Thursday morning with a preliminary magnitude of 6.8, the US Geological Survey said.
It hit about 240 kilometres south of Padang at a depth of just under 24 kilometres. Shallow, inland earthquakes generally are more destructive. There were reports that the second quake badly damaged dozens of additional buildings.
In Padang, the capital of West Sumatra province, the shaking was so intense from Wednesday's temblor that people crouched or sat on the street to avoid falling.
Children screamed as an exodus of thousands of frantic residents fled the coast in cars and motorbikes, honking horns.
At least 500 buildings in Padang collapsed or were badly damaged, said Disaster Management Agency spokesman Priyadi Kardono, adding that 200 bodies had been pulled from the rubble there.
The extent of damage in surrounding areas was still unclear due to poor communications.
Indonesia, a poor, sprawling nation with limited resources, was cobbling together an emergency aid response, and the government was preparing for the possibility of thousands of deaths.
Padang's mayor appealed for assistance on Indonesian radio station el-Shinta. "We are overwhelmed with victims and ... lack of clean water, electricity and telecommunications," Mayor Fauzi Bahar said.
"We really need help. We call on people to come to Padang to evacuate bodies and help the injured."
Hundreds of people were trapped under collapsed buildings in Padang alone, including a four-star hotel, he said. Other collapsed or seriously damaged buildings included hospitals, mosques, a school and a mall.
"I was studying math with my friends when suddenly a powerful earthquake destroyed everything around me," an unidentified boy told the TVOne broadcaster. He escaped out of the top floor just as the three-storey structure, used for after-school classes, crumpled.
TV footage showed heavy equipment breaking through layers of cement in search of more than 30 children it said were missing and feared dead.
Thousands were believed trapped throughout the province, said Rustam Pakaya, head of the Health Ministry's crisis centre.
Search and rescue teams were working in heavy rain when the second strong quake struck, causing widespread panic and badly damaging 30 houses in Jambi, another Sumatran town.
It was not yet clear if there were injuries, said Jambi Mayor Hasfiah, who uses only one name, like many Indonesians.
Frantic parents were seen rushing to local schools in search of their children.
"This is a high-scale disaster," Health Minister Siti Fadilah Supari told Metro TV, referring to the Wednesday quake.
The first quake struck just off the coast of Padang, the US Geological Survey reported. It occurred a day after a killer tsunami hit islands in the South Pacific and was along the same fault line that spawned the 2004 Asian tsunami that killed 230,000 people in a dozen nations.
A tsunami warning was issued Wednesday for countries along the Indian Ocean, but was lifted after about an hour; there were no reports of giant waves.
The shaking in Padang felled trees and crushed cars. A foot could be seen sticking out from one pile of rubble.
At daybreak, residents used their bare hands to search for survivors, pulling at the wreckage and tossing it away piece by piece.
"People ran to high ground," said Kasmiati, who lives on the coast near the quake's epicentre. "I was outside, so I am safe, but my children at home were injured," she said before her cell phone went dead.
The loss of telephone service deepened the worries of those outside the stricken area.
"I want to know what happened to my sister and her husband," said Fitra Jaya, who owns a house in downtown Padang and was in Jakarta when the quake hit. "I tried to call my family there, but I could not reach anyone at all."
Hospitals struggled to treat the injured as their relatives hovered nearby.
Indonesia's government announced US$10 ($NZ13.8) million in emergency response aid and medical teams and military planes were being dispatched to set up field hospitals and distribute tents, medicine and food rations.
Local television reported more than two dozen landslides in the province. Some blocked roads, causing miles-long traffic jams of cars and trucks.
