"It is unfortunate that we have lost 51 people," Kenya's police chief Joseph Boinnet told Capital FM radio.
Three, including Portugese national, killed as van plunges into ravine in Swabi
According to police, the bus was travelling from Nairobi to the western town of Kakamega and carrying 52 passengers.
The Kenyan Red Cross wrote on Twitter that it had overturned. However more details on the cause of the accident were not immediately available.
Bus overturns at Fort Tenan near Kipkelion, several casualties reported. @EMS_Kenya ambulance team activated.
— Kenya Red Cross (@KenyaRedCross) October 10, 2018
Footage from the scene showed the faded red bus lying on its side, the seats and mangled bits of metal exposed to the air with the torn-off roof lying at a distance.
Dozens of people milled around the accident site and goods were strewn over a large area.
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Official statistics show that around 3,000 people die annually in road accidents in Kenya, but the World Health Organisation estimates the figure could be as high as 12,000.
In December 2017, 36 people died in a head-on collision between a bus and a lorry.
In 2016 more than 40 people died when an out-of-control fuel tanker ploughed into vehicles and then exploded on a busy highway.
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