"The water [from the dam burst] has caused huge destruction of both life and property".
In a statement to newsrooms, area Governor Lee Kinyanjui said 15 ambulances have been dispatched to the scene to evacuate victims.
Local television channel KTN News reported that 20 bodies have been recovered so far.
Last week, at least 12 people were killed when a building collapsed during torrential rains in Nairobi. Local officials say neither the extent of the damage nor the death toll are yet clear.
This image shows a child being rescued after a dam failed near the town of Solai, Kenya, on May 9, 2018.More news: Brandon man killed in Maryland shooting
Hundreds of people are said to have been left homeless.
The rescue mission was called off at 2am due to darkness but resumed on Thursday morning.
The mega dam is one of the three water reservoirs owned by a large-scale irrigation farmer, Mr Mansukul Patel, who was not around at the time of the tragedy.
Statistics released by the Interior Principal Secretary Karanja Kibicho on Wednesday indicated that 222,456 people have so far been displaced as a result of ongoing rains in flood-prone areas.
Kinyanjui assured residents that "we will do our best to take affected families to safety and help them get medical attention".
The Red Cross reports that more than 260,000 Kenyans have been displaced by the rains, which came after a gruesome drought.