Dozens of people were reported to be still trapped in the rubble of a hotel in the city of Palu, which was hit by waves up to six metres high following the 7.5 magnitude natural disaster on Friday.
The tsunami, which followed a magnitude-7.5 quake, swept away buildings and unsuspecting victims caught in its path.
"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.
The tsunami was "about three meters high", Nugroho said.
"We are having difficulty deploying heavy equipment. because numerous roads leading to Palu city are damaged", he was quoted by the Kompas newspaper as saying. Around 16,700 people were evacuated to 24 centres in Palu. The water smashed into buildings and a large mosque already damaged by the quake.
Aftershocks continued to rock the coastal city on Saturday.
"It is not just the people in the large urban areas".
The national search and rescue agency would deploy a large ship and helicopters to aid with the operation, said agency chief Muhammad Syaugi, adding that he had not been able to contact his team in Palu.
The city is built around a narrow bay that apparently magnified the force of the tsunami waters as they raced into the tight inlet.
Bodies of some victims were found trapped under the rubble of collapsed buildings, he said, adding 540 people were injured and 29 were missing.
Dozens of injured people were being treated in tents set up in the open.
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The Red Cross is concerned for residents living in an area called Donggala, which is closer to the epicenter of the quake.
"The cut to telecommunications and darkness are hampering efforts to obtain information", he said. Catholic Relief Services' partners were trying to drive to Palu, she said, but only made it halfway there and had to resume travel in the morning.
"We have heard nothing from Donggala and this is extremely worrying", Gelfand said.
The Red Cross estimates that more than 1.6 million people in total could have been affected by the disasters.
The tsunami triggered by a magnitude 7.5 natural disaster smashed into two cities and several settlements on Sulawesi island at dusk Friday. 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.
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. Within minutes a wall of water crashes onto the shore, carrying away buildings and cars.
Elsewhere, rescue teams confronted washed out roads and bridges as they tried to reach another city, Donggala, and other areas completely cut off by the quake and tsunami.
The city's airport was also closed after its runway and a control tower were damaged in the quake.
President Joko Widodo had mobilised the Indonesian military and police to assist in rescue operations in Palu and Donggala, and more troops are expected to arrive soon.
Indonesia sits on the seismically Pacific Ring of Fire and is regularly hit by earthquakes.
The shallow 7.5 magnitude tremor was more powerful than a series of quakes that killed hundreds on the Indonesian island of Lombok in July and August.