The quake brought down hotels, shopping malls and thousands of houses in Palu, while tsunami waves as high as six metres (20 feet) scoured its beachfront shortly afterwards.
About 1,700 houses in one neighbourhood alone were swallowed up by ground liquefaction, which happens when soil shaken by an earthquake behaves like a liquid, and hundreds of people are believed to have perished, the disaster agency said.
Adding to Sulawesi's woes, the Soputan volcano in the north of the island, about 600 km (375 miles) northeast of Palu, erupted early on Wednesday but there were no reports of any casualties or damage. Ash was not expected to disrupt flights.
But concern is growing about conditions in remote areas, many of which have been cut off by destroyed road, landslides and downed bridges.
Aid worker Lian Gogali said the situation in badly hit Donggala district was very difficult.
"Everyone is desperate for food and water. There's no food, water, or gasoline. The government is missing," she said.
She said her aid group had been sending in a trickle of rations into the district of some 300,000 people by motorbike.
The national disaster agency has said tents, food, water and sanitation facilities for more than 60,000 displaced people are in short supply.
Police have done little to stop outbreaks of looting. The government has played down the problem, saying victims could take essentials and shops would be compensated.
The government has said it would accept offers of international aid, after shunning outside help this year when two major earthquakes struck Lombok island, south of Sulawesi.
U.S. President Donald Trump extended condolences in a phone call with Widodo, State Department spokeswoman Heather Nauert told reporters in Washington. The United States has provided initial funding, deployed government disaster experts and was working to determine what other help can be given, she said.
Sitting on the seismically active Pacific Ring of Fire, Indonesia is one of the world's most vulnerable countries to quakes and tsunamis. A quake in 2004 triggered a tsunami across the Indian Ocean that killed 226,000 people in 13 countries, including more than 120,000 in Indonesia.