A team of Kenya Navy divers are helping with the search and recovery efforts.
In a video seen by the Star, the bus driver attempted to steer the vehicle through a flooded section of a bridge on river Enziu.
After a few seconds, the bus was overcame by raging waters and swept into the river. It was not immediately established how many people were aboard the 54 seater-bus.
Mwingi East sub county police commander Joseph Yakan confirmed the incident saying the victims were members of Mwingi Catholic Church who were going for a wedding.
They were travelling in a bus belonging to St Joseph's Seminary, Mwingi.
“Unfortunately the bus was carried by water at Enziu River along Nguni-Nuu road,” he said.
The video showed some passengers trying to swim to safety after escaping from the bus through the windows shortly before it was completely submerged.
Former Kitui Senator David Musila who visited the scene, urged the Kitui County government to erect barriers on the Enziu bridge to avert such accidents in the future.
Machakos governor Alfred Mutua dispatched a team of Emergency and Rescue Service providers to assist in the rescue and recovery efforts.
Mutua also condoled with the bereaved families who lost their loved ones in the accident.
"I also pass my condolence message to my colleague governor, Charity Ngilu following this very tragic incident," he said.
Mutua urged drivers to observe caution while approaching rivers especially during this rainy season.
"All drivers, at this moment, whenever a river is covered by water...even one inch of water is enough to get a bus or a car going. Please do not play with water," Mutua said.
"Just wait until the water subsides. It's better than losing so many lives," he added.
Kenya's Ambassador to Uganda, Kiema Kilonzo also sent his condolences following the incident.
"I stand with you and and pray for you during this difficult moment. May our good Lord comfort you," Kiema said.
He called on the Kitui County government to prioritize construction of proper bridges, especially those in rural areas.
"We can and should save lives as a priority to our county," he said.
Former Kitui governor Julius Malombe also sent his condolences.
This story was last updated at 9 pm, Dec 4.
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