Saturday's landslide flattened dozens of homes of people living in the Koshe dump when part of the largest pile of rubbish collapsed, an AFP journalist said.
Dagmawit Moges, head of the city communications bureau, said 46 people had died -- 32 female and 14 male, including some children.
Many of the victims were squatters who scavenged for a living in the 30-hectare (74-acre) dump, she said.
"When we came out, something like a tornado is rushing to us. We started to collect family members" and escape, he said. "People helped. My child and family left before the destruction happened."
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The streets in the neighbourhood below were filled with women sobbing and wailing.
Bystanders said there were still people trapped under collapsed mounds of rubbish, but police were preventing locals from getting close to the site.
Just six people were seen digging through the rubbish on Sunday looking for survivors and bodies.
He estimated that more than 300 people live on the landfill.
Construction materials, wooden sticks and plastic sheeting could be seen in the wreckage, the AFP journalist said.
For more than 40 years the Koshe site has been the main garbage dump for Addis Ababa, a rapidly growing city of some four million people.
According to local residents, some 50 houses with about seven people living in each of them were built on the trash.
People had built the houses about two to three years ago, said Berhanu Degefe, a rubbish collector who lives at the dump but whose home was not destroyed.
"This part, all of it went down," he said, gesturing at a huge chunk of the hill that suddenly slid. "A lot of people died last night."
Degefe blamed the collapse on a new biogas plant being constructed on top of the hill.
The AFP journalist saw bulldozers on top of the hill pushing piles of rubbish around.
Degefe said they were levelling ground for the plant, increasing pressure on the hillside and causing the collapse.
Mohammed also blamed the biogas plant construction for the tragedy, saying trash had been compressed and the landslide happened "because a lot of garbage is dumped on the top level" and "pressed... Down".