Bereaved families scuffled with rescue workers on Tuesday at a dump in the Ethiopian capital where the collapse of a mountain of rubbish killed at least 82 people on Saturday.

Relatives pushed and shoved emergency workers, angrily accusing them of delays and saying dozens of people were still missing after the disaster at the Reppi dump.

"Nobody is helping us. We are doing all the digging ourselves. It is shameful," Kaleab Tsegaye, a relative of one victim, told the Reuters news agency.

Ethiopia on Tuesday declared three days of national mourning that will be observed from tomorrow.

The collapse late on Saturday destroyed 49 makeshift homes inside the landfill site on the outskirts of Addis Ababa, city spokesman Amare Mekonen said.

Over the past few days, a few rescuers have used bulldozers to move piles of rubbish as hundreds of people have gathered at the scene, weeping and praying. Some dug through the rubbish with their hands.

"My babies, my babies, my little daughter," cried one man wandering through the dump in the Ethiopian capital on Monday, tears streaming down his face. Neighbours said he had lost his wife and four children.

On one side of the hill, volunteers sobbed as they pulled out three corpses, including a child found on top of its mother.

Hundreds of people live on the 50-year-old Reppi dump, the capital's only landfill site, scavenging for food and items they can sell such as recyclable metal.

It was not immediately clear what caused the collapse.

"We expect the number of victims to increase because the landslide covered a relatively large area," Dagmawit Moges, head of the city's communications bureau, said.

About 150 people were at the site when the landslide happened, resident Assefa Teklemahimanot told The Associated Press news agency.

Addis Ababa Mayor Diriba Kuma said 37 people had been rescued and were receiving medical treatment.

"In the long run, we will conduct a resettling programme to relocate people who live in and around the landfill," he said.

"My house was right inside there," said a shaken Tebeju Asres, pointing to where one of the excavators was digging in deep, black mud. "My mother and three of my sisters were there when the landslide happened. Now, I don't know the fate of all of them."

Residents blast government

The resumption of dumping at the site in recent months most likely caused the landslide, Assefa said.

Dumping had stopped in recent years, but it resumed after farmers in a nearby region, where a new landfill complex was being built, blocked dumping in their area.

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Smaller landslides have occurred at the Koshe landfill in the past two years, Assefa said.

Some volunteers had also expressed anger at the city administration on Monday as media arrived at the scene. As well as the two excavators, only three ambulance workers were at the site. Scuffles broke out between them and residents as journalists approached.

"Stop pretending for the cameras!" one local said. "They haven't provided us with anything. Not even gloves. When it gets dark, we are using our mobile phones [for light]."

"We have warned the authorities for more than 10 years as the rubbish piled up. There has not been any response. It is criminal negligence," said Taye Woldeamanuel, a 48-year-old whose sister narrowly survived the landslide.

About 500 waste-pickers are believed to work at the landfill every day, sorting through waste from the capital's estimated four million residents. City officials say close to 300,000 tonnes of waste are collected each year from the capital, most of it dumped at the landfill.

City officials had warned that the site was running out of room and in recent years had been trying to turn the rubbish into a source of clean energy with a $120m investment.

The Koshe waste-to-energy facility, which has been under construction since 2013, is expected to generate 50 megawatts of electricity upon completion.