The officials said work to fix roads and bridges is underway and there are attempts to reach stricken areas by air and sea as well.
In the city - home to around 350,000 people - partially covered bodies lay on the ground near the shore, the day after tsunami waves 1.5 metres (five feet) came ashore.
Authorities said Saturday hundreds of people were on the beach in Palu for a festival when the natural disaster and tsunami struck, sweeping many away to their deaths in the giant waves.
Bodies of some victims were found trapped under the rubble of collapsed buildings, he said, adding 540 people were injured and 29 were missing.
Donggala is also believed to have suffered heavy damage from the tsunami.
Indonesian TV showed dramatic smartphone video of a powerful wave hitting Palu, with people screaming and running in fear.
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.
Nugroho tweeted that Indonesia's military has been mobilized to assist search and rescue teams. He said the woman told him that four of her children had been swept away by the tsunami.
People living hundreds of kilometres from the epicentre reported feeling the massive shake, hours after a smaller jolt killed at least one person in the same part of the Southeast Asian archipelago. "We all panicked and ran out of the house" when the quake hit, said Anser Bachmid, a 39-year-old Palu resident. Such shallow quakes tend to be more destructive.
Pictures supplied by the agency showed a badly damaged shopping mall in Palu where at least one floor had collapsed onto the storey below, while other photographs showed major damage to buildings and large cracks across pavements.
The agency also said homes and a local hotel were flattened while a landmark city bridge was destroyed.
About 17,000 people had been evacuated, the disaster agency said.
The city's airport has been reopened only for relief efforts and will remain closed until October 4 for commercial flights, Nugroho said.
Friday's tremor was centred 78 kilometers north of Palu, the capital of Central Sulawesi province, but was felt in the far south of the island in its largest city Makassar and on the neighbouring island of Kalimantan, Indonesia's portion of Borneo island. But rescuers worry that they could find more victims of the disaster in the Donggala region, which is closer to the epicenter of the quake.
Indonesia, the world's most populous Muslim country, is frequently hit by earthquakes, volcanic eruptions and tsunamis because of its location on the "Ring of Fire", an arc of volcanoes and fault lines in the Pacific Basin. On Aug. 5, a powerful quake on the Indonesian island of Lombok killed 505 people, most of whom died in collapsing buildings.
In December 2004, a massive magnitude 9.1 natural disaster off Sumatra in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.
Indonesia's meteorological and geophysics agency BMKG issued a tsunami warning after the quake, but lifted it 34 minutes later.
This is published unedited from the PTI feed.