City officials have reportedly been trying to find a new site for years.
A massive mound of trash collapsed late Friday night, burying homes on the edge of the site as residents slept, Reuters reported.
The death toll on Saturday was listed as eight, including two children.
Kampala police spokesman Patrick Onyango told AFP on Sunday that four more bodies had been recovered and 14 people had been rescued.
“Rescue efforts will continue until we can confirm that no one is trapped,” he said.
Mr Onyango said the landslide forced about 1,000 people from their homes. He did not specify how many people were living at the site or nearby.
Many people make a living by scavenging through trash heaps for resellable items.
The Uganda Red Cross has been providing tents to those in need of temporary shelter.
