"The rain that fell last night caused disaster in the Northern and Western Provinces," RBA said on its website.
"Currently, the provisional figures published by the administration of these provinces say that 109 people have been declared dead."
The broadcaster said the floodwaters were still rising, "causing a threat to more lives".
It said 95 people had perished in the hardest-hit Western Province and another 14 in Northern Province, adding that the floodwaters had swept away homes and infrastructure and led to road closures.
Images broadcast on RBA's Twitter account showed houses destroyed, roads cut off by landslides and flooded fields.
"Relief efforts began immediately, including helping to bury victims of the disaster and providing supplies to those whose homes were destroyed," the minister in charge of emergency management, Marie Solange Kayisire, told RBA.
She called on local residents to increase patrols, especially at night, so people could be moved to safer ground when it rains heavily.
In neighbouring Uganda, six people died in the west of the country when landslides struck their homes after days of torrential rain, according to the local Red Cross.
It said five of the dead belonged to the same family and were from a single village.
In May 2020, at least 65 people died in Rwanda as heavy rains pounded East Africa, while at least 194 deaths were reported in Kenya.
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