Many of the victims were swept away by giant waves as they played on the beach.
Strong aftershocks continued to rock the coastal city on Saturday morning after waves up to six metres (18 feet) high swept through the scenic tourist town on Friday, triggered by a 7.5 magnitude earthquake on land.
"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, spokesman of Indonesia's disaster mitigation agency BNPB said in news briefing in Jakarta.
Hundreds of people were preparing for a beach festival to celebrate Palu's anniversary. The festival was due to start Friday night.
Some people climbed six metre (18 feet) trees to escape the tsunami and survived, Nugroho said.
Photos confirmed by authorities showed bodies being lined up along the street on Saturday, some in bags and some with their faces covered with clothes.
Amateur footage shown by local TV stations, which could not immediately be authenticated by Reuters, showed waters crashing into houses along Palu's shoreline, scattering shipping containers and flooding into a mosque in the city.
Nugroho described the damage as "extensive" with thousands of houses, hospitals, shopping malls and hotels collapsed, a bridge washed away and the main highway to Palu cut due to a landslide.
Bodies of some victims were found trapped under the rubble of collapsed buildings, he said, adding 540 people were injured. Dozens of injured people were being treated in makeshift medical tents set up outdoors, TV images showed.
Indonesia's meteorological and geophysics agency BMKG issued a tsunami warning after the quake, but lifted it 34 minutes later. The agency has been widely criticised for not informing a tsunami had hit Palu on Saturday, though officials said waves had come within the time the warning was issued.
The quake and tsunami caused a major power outage that cut communications around Palu and on Saturday authorities were still having difficulties coordinating rescue efforts.
The disaster mitigation agency has not been able to get any information from the fishing town of Donggala, closer to the epicentre of the quake 27 km (16 miles) away. More than 600,000 people live in Donggala and Palu.
Chief security minister Wiranto told TVOne the military had started sending in cargo planes from the capital Jakarta carrying relief aid.
The city's airport remained closed after its runway and air traffic control tower was damaged in the quake but officials said they were preparing to reopen to allow aid to come in.
Nugroho, spokesman for the disaster mitigation agency, said no command centre for disaster recovery has been created yet.
The Palu area was hit by a less powerful quake earlier on Friday, which destroyed some houses, killed one person and injured at least 10 in Donggala, authorities said.
The U.S. Geological Survey put the magnitude of the second quake at a strong 7.5, after first saying it was 7.7.
Indonesia sits on the Pacific Ring of Fire and is regularly hit by earthquakes. In August, a series of major quakes killed over 500 people in the tourist island of Lombok and destroyed dozens of villages along its northern coast.
Palu was hit by tsunami in 1927 and 1968, according to BNPB.