Villagers in a region close to the city of Palu where the tsunami hit, are reportedly still pulling out loved ones, both dead and alive, from the mud.
Indonesian President Joko "Jokowi" Widodo has given permission for the country to accept international help.
The natural disaster has killed 844 people and displaced nearly 50,000 people, according to Indonesia's disaster agency.
Amid the devastation, there was a small glimmer of hope as rescuers pulled a 38-year-old man out alive from beneath a collapsed building three days after disaster struck Palu.
According to local media reports, the man was said to be conscious and talking to his rescuers as they worked by flashlight.
Acts of heroism are also emerging as locals report the bravery of fellow Indonesians who have saved lives.
A 21-year-old air traffic controller has been hailed a hero after losing his own life to ensure a passenger plane escaped the 7.5 magnitude quake that rocked the nation on Friday.
The pilot who was communicating with controller, Anthonius Gunawan Agung, said he jumped from the crumbling tower, which eventually killed him.
"Thank you for keeping me and guarding me till I’m safely airborne".
For those closest to the tsunami, the reality was a terrifying one.
In the aftermath of the quake, Palu's residents told ITV News Senior International Correspondent John Irvine about how they were hit by a "tsunami of mud".
Aid agencies respond to the extent of disaster
Survivors are also grappling with dwindling supplies of food and water.
According to local television reports around 3,000 residents had flocked to the Palu airport trying to get out.
With the airport only resuming some commercial flights, footage showed some people screaming in anger because they were not able to board departing military aircraft.
One woman shouted: "We have not eaten for three days!
"We just want to be safe!"
Many are still coming to terms with the loss of everything they owned.
Footage captured on a mobile phone shows a family desperately trying to stay together the moment the earthquake struck, shaking the ground beneath them.
In bid to reach those trapped in the hard-hit cities of Palu and Donggala, troops boarded a naval ship on Monday morning.
They'll join some 1,300 personnel already at site, including military and police.
They are bringing food, water and other supplies to the affected area.
President Widodo said the European Union and 10 countries have offered assistance, including the United States, Australia and China.
The UK are sending a team of five people to help with rescue efforts "on the ground" and giving £2 million in aid money to help "meet the needs of the most vulnerable people".
International Development Secretary Penny Mordaunt said: “Following a request from the Government of Indonesia this morning, we are deploying a team of UK aid humanitarian advisers to the region who will use their disaster response expertise to help co-ordinate efforts on the ground".
But aid agencies have said "the biggest problem" they face is getting access to hard hit areas.
Save The Children's Tom Howells said a "lot of agencies like ourselves" are "struggling to get to areas that are most affected".
Military assists with mass burials and the digging of trenches
Mass graves have been dug as the death toll rises and military personnel are helping with the digging of trenches and burials.
Local army commander, Tiopan Aritonang, said he is expecting 545 bodies for the grave from one hospital alone.
All of the victims, coming from local hospitals, have been photographed to help families locate where their relatives were buried.
Indonesia's National Disaster Mitigation Agency is pushing for burials to be done "as soon as possible for health and religious reasons".
Indonesia is majority Muslim, and religious custom calls for burials soon after death, typically within one day.
Willem Rampangilei, chief of Indonesia's National Disaster Mitigation Agency, said the trench dug in Palu was 10 metres by 100 metres (33 feet by 330 feet) and can be enlarged if needed.
The earthquake struck the Indonesian island of Sulawesi on Friday.
Most of the dead were from the city of Palu, but much is still unknown about other coastal towns that have yet to be properly assessed due to impassable roads, downed power lines and phone outages.
In Donggala, the site closest to the earthquake's epicentre, aerial footage on Metro TV showed the blond sands of beaches swept out to sea, along with some buildings.
Some buildings in the town were severely damaged, with plywood walls shredded and chunks of concrete scattered on the pavement.
Much of the damage, however, appeared limited to the waterfront.
Palu, which has more than 380,000 people, was strewn with debris from the earthquake and tsunami.
A heavily-damaged mosque was half submerged and a shopping mall was reduced to a crumpled hulk.
A large bridge with yellow arches had collapsed.
The city is built around a narrow bay that apparently magnified the force of the tsunami as the waves raced into the tight inlet.
In one devastated area in Palu, residents said dozens of people could still be buried in their homes.
Local resident Nur Indah said: "The ground rose up like a spine and suddenly fell.
"Many people were trapped and buried under collapsed houses. I could do nothing to help.
"In the evening, some of them turned on their mobile phones just to give a sign that they were there. But the lights were off later and the next day."