There were also concerns over the whereabouts of hundreds of people preparing for a beach festival that had been due to start on Friday evening, the agency said.
Authorities expect the toll to rise sharply today as news arrives from remote areas.
A man stands amid the damage caused by the tsunami.
But instead of fleeing, he stayed on the job to ensure a plane carrying hundreds of passengers took off safely, The Sun reports.
A YOUNG air traffic controller who sacrificed himself to guide an aircraft to safety during Indonesia's devastating 7.5 quake and tsunami has been hailed a hero.
Indonesian television and other media, citing disaster agency spokesman Sutopo Purwo Nugroho, says the death toll from the Sulawesi quake and tsunami has jumped to 384.
Baptiste Gombert, a geophysics researcher at University of Oxford, said it was "surprising" the quake had generated a tsunami.
Rescue officials on Saturday were struggling with poor communications, widespread outages, destroyed bridges and blocked roads.
It's believed the tsunami, confirmed by local agencies to be up to 10 feet tall, struck Donggala and Palu, a coastal town of about 330,000 after the alert was cancelled. Officials said more than 380 were dead in Palu alone, and more were unaccounted for.
More than 600,000 people live in Donggala and Palu.
"This is already a tragedy, but it could get much worse".
Patrick Kielty's Twitter rant at Boris Johnson's 'Brexit lies' Brexit
Numerous earthquakes have struck the region in recent months.
Last month, a powerful natural disaster hit the island of Lombok, followed by a series of strong quakes throughout the month.
Commercial flights to Palu were going to be suspended until October 4, with only emergency and humanitarian flights allowed to land, but the Indonesian government announced later on Saturday the airport would reopen for commercial flights on Sunday. But the organisation still had many of its staff members in Lombok responding to the destruction and widespread loss of homes there. Palu's airport was closed Saturday, its runway badly cracked from the quake.
The city is built around a narrow bay that apparently magnified the force of the tsunami waters as they raced into the tight inlet.
The Indonesian military and police have set up field hospitals in Palu but relief and rescue efforts are expected to be ramped up in the days ahead.
'I heard people shouting Water!
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.
Hospitals in Palu were swamped with patients who had to lie on the ground hooked to drips.
About 17,000 people had been evacuated, the disaster agency said.
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.
A magnitude 7.5 natural disaster spawned a deadly tsunami on Friday evening, killing more than 400.
Mr Haris is among the survivors of Indonesia's latest natural disaster.