"Preliminary investigations show that the accident is due to speeding," regional police chief Charles Mkumbo told the state-run Tanzania Broadcasting Corporation late on Saturday.
Some reports said the people on the bus were not wearing seat belts at the time of the crash.
The accident happened early on Saturday when the bus went off the road and into the Marera river gorge in Karatu district near the northern city of Arusha where the children were attending Lucky Vincent Primary School.
The final year primary pupils were on their way to sit mock examinations ahead of seeking places at secondary school.
"It's a huge tragedy," Innocent Mushi, the school's director said.
President John Magufuli sent his condolences to the families of the dead.
"This accident extinguishes the dreams of these children who were preparing to serve the nation, it is an immense pain for the families involved and for the whole nation," Magufuli said in a statement.
Speeding is the cause of most road accidents in Tanzania, according police statistics that show around 3,000 people killed each year.
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