CNN  — 

A young mother who had to flee with her newborn child is one of thousands of survivors from Sunday’s deadly earthquake on the Indonesian island of Lombok desperately waiting for aid to trickle through.

The death toll from the 6.9-magnitude quake has risen to 347, and is expected to be higher once all the bodies can be counted, according to the state-run Antara news agency.

Aid is beginning to reach the northern parts of the island, which were among the worst hit by the quake, but witnesses on the ground in Kayangan said hundreds of people – many young children and elderly – are still waiting for help to reach their area. They are currently sleeping outside, some subsisting on crackers and chili sauce as food supplies run out.

Sumiati, 27, was giving birth as the quake hit, and had to flee with her one day old baby to an evacuation spot.

“When the quake happened, I took my kid and ran,” she said. “The electricity was off, but it went back on, I grabbed my kid then ran out to save us from the rubble.”

Sumiati returned to her home to survey the damage and found the roof partially collapsed.

More than 120 people died in Kayangan as a result of the quake, according to the state-run Antara news agency. On Tuesday, the government estimated up to 20,000 people were still in need of assistance in northern Lombok, with around 80% of buildings destroyed.

Sumiati and her baby are among the survivors waiting for aid. “I know stay in the evacuation spot,” she said. “It’s cold at night and very hot during the day.”

“We need diapers, we lack everything, I’m afraid my baby would get sick,” she added. “I’m very worried, we need help here.”

Survivors of Sunday's earthquake, including small children and elderly people, are running out of food as aid struggles to get through.

The Red Cross previously said aid was struggling to reach the northern parts of the island due to debris from the quake and the ongoing risk of landslides.

“A lot of people are displaced, and many have migrated to the hilly and mountainous areas because of fear of a tsunami,” Red Cross representative Husni Husni said.

At Tanjung Public Hospital in northern Lombok, its seven ambulances were in heavy use, but one is already out of action due to lack of fuel.

Full impact of the quake is unclear

As relief agencies get to work on the ground, they warned the full impact of the earthquake may take days to become known.

“We are still waiting for assessments from some of the more remote areas in the north of the island, but it is already clear that Sunday’s earthquake was exceptionally destructive,” Christopher Rassi, the head of the assessment team for the International Federation of Red Cross and Red Crescent Societies, said in a statement.

Despite the mammoth recovery efforts ahead, Indonesia’s National Disaster Management Agency said Wednesday that international aid was not yet needed.

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A man stands near the ruins of a collapsed house on Lombok island on Wednesday.

Tourists evacuated

Meanwhile, the Red Cross said Tuesday all of the 2,000 tourists on the Gili Islands had now been evacuated.

Dramatic video tweeted by authorities showed hundreds of people, many believed to be foreign vacationers, crammed onto a beach on the island of Gili Trawangan as evacuation measures got underway.

Emergency personnel raced to evacuate tourists from the three small islands, famous for their white sandy beaches and clear waters, which are near the epicenter of the quake on Lombok.

For residents of Lombok and surrounding islands, many saw their homes destroyed, with the collapse of roofs and walls causing the majority of casualties from the quake.

Gusti Lanang Wisnuwandana, an official with the Mataram Search and Relief Office, told Antara that medical and rescue workers were struggling to deal with survivors terrified of being indoors after the quake.

“They are still traumatized. Most of them are not willing to stay in the building while they are undergoing (an) operation or after they have undergone (an) operation. They want to be treated outdoors,” he said, adding that search and rescue work was still ongoing.

“Today, we managed to find one dead victim buried under the rubble of a building in Sigar Penjalin village.”

CNN’s Hilary Clarke, Angela Dewan, Josh Berlinger, Lauren Said-Moorhouse and James Griffiths contributed to this report.