The 7.6 magnitude undersea quake struck on Wednesday evening, about 50km from the coastal city of Padang with a population of 900,000.
A second quake, with a 6.8 magnitude, struck Sumatra on Thursday morning, about 225km southeast of Padang, according to the US Geological Survey.
Search and rescue teams were working in heavy rain in Padang when the second quake struck, causing widespread panic and badly damaging 30 houses in Jambi, another Sumatran town.
It was not yet clear if there were injuries, Hasfiah, Jambi's mayor, said.
Raphael Abreu, a geophysicist with the US Geological Survey in Colorado, told Al Jazeera that the second quake was "definitely capable of creating, by itself, significant damage to structures and property.
"And if combined with weakened situation in places like Padang which is still suffering the effects of the earlier quake, it could definitely compound the already significant damage in Padang".
Fauzi Bahar, Padang's mayor, appealed for assistance on Indonesian radio station el-Shinta, saying the city was "overwhelmed".
"We really need help. We call on people to come to Padang to evacuate bodies and help the injured," he said.
Susilo Bambang Yudhoyono, Indonesia's president, instructed officials to "flood" Padang with aid and medical relief, while his government announced $10m in emergency aid.
Al Jazeera's Step Vaessen, reporting from Padang on Thursday, said the airport - closed the day before due to damage caused by the quake - had been reopened.
Medical teams and military aircraft were arriving with field hospitals, tents, medicine and food rations as officials ramped up the rescue and relief operation.
Officials in Padang said about 500 houses had caved in and witnesses said many buildings had collapsed after Wednesday's quake.
Priyadi Kardono, a spokesman for Indonesia's disaster management agency, said the effects of Wednesday's quake "could be as big as the Yogyakarta quake", referring to a 2006 disaster that killed more than 5,000 people and damaged or destroyed 150,000 homes.
At daybreak on Thursday, residents used their bare hands to search for survivors.
Survivors were seen being pulled from the rubble and hospitals struggled to treat the many injured.
Panicked residents rushed from their homes on to the streets after Wednesday's quake struck off Sumatra's west coast at 5:16pm local time (10:16 GMT).
It was felt in the Indonesian capital Jakarta, 940km away, and sent frightened office workers streaming out of buildings in Singapore as well as Malaysia's capital, Kuala Lumpur.
Dozens of aftershocks followed.
The Pacific Tsunami Warning Centre issued a regional tsunami warning, but cancelled it afterwards.
'Ring of Fire'
The Indonesian earthquake came just hours after a series of tsunamis on the Pacific islands of American Samoa and Samoa left more than 100 people dead.
Padang, the capital of Indonesia's West Sumatra province, sits on one of the world's most active fault lines along the so-called Ring of Fire, the same one that cracked off Aceh, at the northern tip of Sumatra, in 2004 to trigger the Indian Ocean tsunami.
|Shopping malls, hospitals and hotels in Padang were among the structures toppled [Reuters]
That disaster killed more than 220,000 people in Indonesia, Thailand, Sri Lanka and India among other countries.
Padang was badly hit by an 8.4 magnitude quake in September 2007, when dozens of people died and several large buildings collapsed.
Scientists had been warning of a major earthquake in the area for a long time, but Jakarta said it did not have funds for disaster-preparation measures, our correspondent said.
And geologists say the low-lying city is vulnerable to more quakes and tsunamis.
"There are three big volcanoes in west Sumatra - Merapi, Talang and Tandikat," Surono, the head of the Geological Disaster Mitigation and Volcanology Centre in Indonesia, said.
"We fear that this quake might cause volcanic eruptions there."