Ten people died after the Patel Dam in Subukia, Nakuru County burst its banks on Wednesday night, sweeping across densely populated villages..
Mr Kinyajui said: "The water has caused huge destruction of both life and property".
"First responders have been on the ground; we commend them for the work they are doing", Esipisu said, adding relevant authorities will issue a comprehensive statement once they have full details.
A local television station said 20 bodies had been recovered so far.
Last week, at least 12 people were killed when a building collapsed during torrential rains in Nairobi. Local officials say the full extent of the damage is not yet clear.
Heavy rainfall and floods have hit East Africa in recent months with Kenya and Rwanda among the worst hit.
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Homes were overrun by the rushing water from the Patel Dam in the town of Solai leading to the death of many residents in the Nakuru County.
A search and rescue operation led by police was set up and includes officers from the National Youth Service (NYS) as well as members of the public. "Looking at families being displaced, children, mothers, the elderly being swept away by floods, it's traumatizing".
"We assure residents that the rescue teams are doing their best to evacuate affected families to safety and assist victims get medical attention", said Mr Mbae.
"The county has dispatched ambulances to the scene to aid in evacuation of victims", he said.