Four adults also died, said Sandeep Kumar, a local official. Ten children were hospitalized.
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Initial reports indicated the bus driver was speeding as he took the children home and lost control at the edge of the gorge. The bus fell some 200 feet (60 meters) to the ground below, said police officer Sunil Kumar.
The adults killed included the bus driver, two teachers and another woman, officials said. Most of the children riding in the bus were believed to be in elementary school.
The crash occurred in the Kangra Valley, about 500 kilometers (300 miles) north of New Delhi.
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The search for survivors ended late Monday night, with the bodies of the dead lying on the concrete floor of the Nurpur mortuary, covered by sheets.
India's roads, particularly in the hills, have long been feared for their deep potholes, reckless drivers and often a lack of guardrails. Fatal accidents are common.
"I am deeply anguished by the loss of lives," Prime Minister Narendra Modi said in a tweet. "My prayers and solidarity with those who lost their near and dear ones."