A young woman was pulled alive from the rubble of the Roa Roa Hotel, the news website Detik.com reported. Hotel owner Ko Jefry told Metro TV on Saturday that up to 60 people were believed trapped. Hundreds of people gathered at the wrecked mall searching for loved ones.
"The Indonesian Red Cross is racing to help survivors but we don't know what they'll find there".
Reports are still coming in of the impact of the disaster on communities further up the coast from Palu and closer to the quake's epicentre, including the smaller town of Donggala, where there was at least one death and 10 people were injured.
AirNav said one of its air traffic controllers, aged 21, died in the quake after staying in the tower to ensure a flight he had just cleared for departure got airborne safely.
"We're now getting limited communications about the destruction in Palu city, but we have heard nothing from Donggala and this is extremely worrying".
"We felt a deep heartbreak, may God gives Anthonius the best place beside him, along with other victims of Donggala natural disaster", said a spokesperson for Air Nav Indonesia, the country's aircraft navigation agency.
Indonesia is all too familiar with deadly earthquakes and tsunamis.
Rescue teams in Indonesia struggled on Sunday to reach communities feared devastated by a major quake and tsunami on Sulawesi island.
Tsunami warning systems set up after the 2004 tsunami - that killed 168,000 people in Indonesia - appeared to have failed.
Meanwhile criticisms have been levelled at the country's geophysics agency for lifting the tsunami warning 34 minutes after it was first issued, which may have led to confusion and exacerbated the death toll. But officials said they estimated the waves had hit while the warning was in force.
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The number of casualties was no doubt increased by the fact that hundreds of people had descended on Palu's beach for a festival to celebrate the city's anniversary, due to start Friday night.
Dramatic video footage captured from the top floor of a parking ramp in Palu, almost 80 kilometers from the quake's epicentre, showed waves bring down several buildings and inundate a large mosque.
In other footage on social media, a man on the upper floor of a building could be heard shouting warnings of the approaching tsunami to people on the street below moments before the wave crashed ashore.
"When the (tsunami) threat arose yesterday, people were still doing their activities on the beach and did not immediately run and they became victims", Sutopo Purwo Nugroho, the spokesman for Indonesia's disaster mitigation agency BNPB said in a briefing in Jakarta.
Officials say rescuers need heavy equipment to shift slabs of broken concrete but access to many areas has been hampered by damaged roads, landslides and collapsed bridges.
Traumatized victims, many of whom were sleeping in tents and being treated for injuries outside their homes, continued to be shaken by aftershocks.
President Joko Widodo is scheduled to visit evacuation centres in Palu on Sunday.
"If he needs our help, he'll have it", Mr Morrison told the ABC on Sunday.
More than half of the 560 inmates in Palu's prison escaped after its walls collapsed during the quake, according to state news agency Antara, while more than 100 inmates escaped from a prison in Donggala.
Though Indonesia is in the Ring of Fire - a roughly 40,234km chain of volcanoes and other tectonic hot spots that stretches across the Pacific Ocean and plays host to 90 per cent of the world's earthquakes - National Geographic reported that the tsunami was unexpected at this quake.
In August, a series of major quakes killed more than 500 people On the tourist island of Lombok, hundreds of kilometres southwest of Sulawesi.