At least six children searching for valuables in the dump are among the missing, he said.
A police spokesman put the death toll at four and said 14 people had disappeared.
Scores of poor people forage for scrap metal and other recyclables despite dangers of landslides during seasonal rainfall.
"Yesterday it rained all afternoon and into the night, saturating the land and causing the landslide," Gerson Contreras, a police spokesman, said.
"Because of the rains and what happened before, the authorities have been trying to stop people from going there, but their need is so great they just kept coming," Contreras said.
Last month, eight people were killed in a similar collapse at Guatemala City's main rubbish dump, located to the south of the capital.