"If he needs our help, he'll have it", Mr Morrison told the ABC on Sunday.
Nugroho said the casualties and the damage could be greater along the coastline 300 km (190 miles) north of Palu, an area called Donggala, which is closer to the epicentre of the quake.
"People were still going about their activities on the beach and did not immediately run", said Sutopo Purwo Nugroho, spokesman for Indonesia's National Disaster Management Agency, adding that the death toll would "continue to rise as the search continues".
Officials say strong aftershocks rocked the city this morning, causing thousands of homes to collapse and damage to hospitals, hotels and a shopping centre.
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".
Dozens of injured people were being treated in makeshift medical tents set up outdoors.
The death toll of anearthquake and tsunami that hit two Indonesia cities has reached at least 384 as rescuers battle to reach victims in devastated areas.
"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.
The nearby cities of Donggala and Mamuju were also ravaged, but little information was available due to damaged roads and disrupted telecommunications.
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"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.
While numerous injured are being treated at local hospitals, according to CNN, at least one hospital has been structurally compromised, resulting in some of the injured being cared for in the street. Hotel owner Ko Jefry told Metro TV on Saturday that up to 60 people were believed trapped.
An early tsunami warning had been issued by the Indonesian meteorological agency, but was later lifted after the agency ascertained that the water had receded.
"I can still hear the voices of the survivors screaming for help while inspecting the compound", he told local online news portal Detik.com, adding there could be 50 people trapped inside.
Questions have been raised about what caused the tsunami, with speculation an underwater landslide was to blame.
Palu was hit by tsunami in 1927 and 1968, according to BNPB.
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.
Vision showed a fast moving wall of water flooding into the city, carrying cars, trees and parts of buildings with it.
- 2004: A major quake on the western coast of Indonesia's Aceh province in northern Sumatra on December 26 triggered a tsunami that struck 14 countries, killing 226,000 people along Indian Ocean coastline, more than half of them in Aceh.
Palu's airport also suffered damages, its runway badly cracked from the quake.
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.