Red Cross said there are more than 300,000 people living in the area, and vice president Jusuf Kalla warned the death toll could rise to thousands.
Bodies of some victims were found trapped under the rubble of collapsed buildings, he said, adding that 540 people were injured.
CNNreports that rescue workers are still searching for survivors after the quake hit the Indonesian island of Sulawesi and triggered a subsequent tsunami.
Many people reported trapped in the rubble of buildings brought down in the 7.5 magnitude natural disaster which struck on Friday and triggered tsunami waves as high as six metres, officials say.
"People were still going about their activities on the beach and did not immediately run", said Sutopo Purwo Nugroho, spokesman for Indonesia's National Disaster Management Agency, who said that hundreds were gathered in Palu for a beach party.
The tremor triggered a tsunami that hit beaches in the cities of Palu and Donggala, officials said.
About 10,000 displaced people were scattered at 50 different places in Palu, he said.
"We got a report over the phone saying that there was a guy who climbed a tree up to 6 meters high", said Nugroho, the disaster agency spokesman.
Donggala is a city of about 270,000 people, while the nearby city of Palu is home to about 330,000 people. A shopping mall was reduced to rubble.
In the nearby city of Donggala, home to almost 300,000 people, a large arched bridge that spanned a coastal river collapsed.
The geography of the city, which sits at the end of a long, narrow bay, could have magnified the size of the tsunami, it said.
Video footage on social media showed a man on the upper floor of a building shouting warnings of the approaching tsunami to people on the street below moments before the wave crashed ashore. The water smashed into buildings and a large mosque already damaged by the natural disaster.
The city's main hospital was damaged in the quake, with TV footage showing dozens of injured people being treated outside in makeshift medical tents. The agency has been widely criticized for not informing a tsunami had hit Palu on Saturday, though officials said waves had come within the time the warning was issued.
Indonesia tsunami and earthquake kill 384, leave hundreds injured
Nugroho has said that essential aircraft can land at Palu airport's, though AirNav, which oversees aircraft navigation, said the runway was cracked and the control tower damaged.
The ruin of a mosque badly damaged by quake and tsunami is seen in Palu, Central Sulawesi, Indonesia.
Road access to Palu from the east and the south are disconnected, making relief efforts hard, authorities said.
Ricoh said there was no immediate plan to search for the inmates because the prison staff and police were consumed with the search and rescue effort.
"Don't even think to find the inmates".
Ms Redstone said the areas hit by the quake and tsunami were densely populated with poor and vulnerable people.
Indonesia's president said on Friday night that he had instructed the security minister to co-ordinate the government's response to the quake and tsunami.
The British Broadcasting Corporation (BBC) reports that rescue efforts are being hampered by a major power cut.
United Nations spokesman Stephane Dujarric said United Nations officials were in contact with Indonesian authorities and "stand ready to provide support as required".
Sulawesi has a history of religious tensions between Muslims and Christians, with violent riots erupting in the town of Poso, not far from Palu, two decades ago.
It lies on the Pacific "Ring of Fire", where tectonic plates collide and numerous world's volcanic eruptions and earthquakes occur.
In December 2004, a massive magnitude 9.1 quake off Sumatra island in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.
In December 2004, a 9.1-magnitude natural disaster off Sumatra in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.
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