The nearby cities of Donggala, the site closest to the earthquake's epicenter, and Mamuju were also ravaged, but little information was available due to damaged roads and disrupted telecommunications.
"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.
Thousands of buildings have collapsed in Palu city, including the four-storey Antapura hospital, the eight-storey Roa-Roa hotel, a shopping mall and a bridge.
Photographs from the city on the coast of Sulawesi island showed bodies being lined up along the street, some in bags and others with their faces covered with clothes.
"We're now getting limited communications about the destruction in Palu city, but we have heard nothing from Donggala and this is extremely worrying", Red Cross said. Dozens of injured people were being treated in makeshift medical tents set up outdoors, TV images showed.
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The current death toll is 420, but rescue teams are now scrabbling to reach the area and it is expected to rise into the thousands.
"We are having difficulty deploying heavy equipment to find victims under the rubble of buildings because numerous roads leading to Palu city are damaged". A bridge was washed away and the main highway to Palu was cut off due to a landslide.
"We felt a deep heartbreak, may God gives Anthonius the best place beside him, along with other victims of Donggala quake", Air Nav spokesperson Yohanes Sirait said. "I was squeezed into the ruins of the wall, I think", said Haris, adding that the family was in town for a wedding.
"It was very hard for the guards to stop the inmates from running away as they were so panicked and had to save themselves too", Antara quoted warden Adhi Yan Ricoh as saying.
"I'm anxious about people who might have been washed away", she added. Officials said more than 380 were dead in Palu alone, and more were unaccounted for.
At the city's Roa-Roa Hotel, which was completely flattened by the quake, many people were still missing. "All we knew is that 24 guests were successfully evacuated and one has died", hotel owner Ko Jefry told Metro TV on Saturday night.
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"People are encouraged to remain vigilant", Sutopo said.
Indonesia's meteorological and geophysics agency BMKG issued a tsunami warning after Friday's quake, but lifted it 34 minutes later. Officials said they were rushing to reopen the airport to allow aid to come in.
The nearby city of Donggala and the town of Mamuju were also ravaged by the magnitude 7.5 natural disaster and tsunami but had not yet been reached by aid due to damaged roads and disrupted telecommunications. Reuters was not able to authenticate the footage.
The military has started sending in aircraft with aid from Jakarta and other cities, authorities said.
Anthonius Gunawan Agung, 21, was the only person left in the control tower at the Air Traffic Tower of Mutiara Sis Al Jufri Airport in Palu when the magnitude-7.5 quake struck the coastal city on Friday.
This latest quake comes after a series of earthquakes in July and August killed at least 623 people and destroyed hundreds of thousands of buildings on the Indonesian island of Lombok, which is situated hundreds of kilometres south-west of Sulawesi.
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People injured or affected by the quake and tsunami in Palu wait to be evacuated.