“The soil was already soaked from the previous days of rain, which led to landslides that blocked roads,” he said.
In a statement, President Paul Kagame said his government was helping those affected, including temporary rehabilitation.
The Uganda Red Cross said six people died on Wednesday night in the southwestern Kisoro district, a mountainous area in neighboring Uganda near the border with Rwanda.
Five were from a family, and emergency crews have begun digging to retrieve bodies, it added in a statement.
Rwanda and Uganda have been receiving heavy and continuous rains since late March. Landslides have been reported in other highlands of Uganda, such as Kasese near the Rwenzori Mountains, where deluge and flooding destroyed homes and displaced hundreds.