After torrential rain in recent weeks, a chunk of garbage from the city's only landfill site broke off late on Friday, crushing and burying homes on the edge of the site as residents slept.
On Saturday, the Kampala Capital City Authority had put the death toll at eight.
"The latest we have is 13 dead, but rescue services are continuing," police spokesperson Patrick Onyango said on Sunday.
At least 14 people have been rescued so far, he said, adding that more could still be trapped but the number was unknown.
Tents have been set up nearby for those displaced by the landslide, Uganda Red Cross said.
The landfill site, known as Kiteezi, has served as Kampala's sole garbage dump for decades and had turned into a big hill.
Residents have long complained of hazardous waste polluting the environment and posing a danger to residents.
Efforts by the city authority to procure a new landfill site have dragged on for years.
There have been similar tragedies elsewhere in Africa from poorly managed mountains of municipal garbage.
In 2017, at least 115 people were killed in Ethiopia, crushed by a landslide at a garbage dump in Addis Ababa.
In Mozambique, at least 17 people died in a similar 2018 disaster in Maputo.
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