The bus driver and two teachers were also killed in the accident on Monday evening.
This publication reports the Hindustan Times, citing local police.
"My first priority was to save lives".
The accident happened near the intersection of Northside Drive and Jett Street on Wednesday morning at 9 a.m. Officials say a vehicle was attempting to change lanes when it hit the rear of another auto, sending it spinning and crashing into the school bus.
Some of the seriously injured have been taken to hospital in Pathankot.
Onlookers rushed to search the mangled yellow bus upturned on the valley slope for survivors.
State would provided all possible help to the affected family as DC Kangra has been directed to ensure all possible assistance to the victims and speedy rescue operation.
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India has some of the world's deadliest roads.
Road accidents are common in India, often due to poor driving or badly maintained roads and vehicles.
Last month, a truck carrying a wedding party drove off a bridge in western India killing 30 people, mostly women, and children. The children killed were all between the ages of 5 and 14 years. "We have been able to account for 38 people on the bus".
An injured student of the school bus that fell into a gorge lies on a hospital bed in Himachal Pradesh, India on April 9, 2018.
Last July, a bus rolled off a cliff around 100 kilometers from Shimla, a hill resort popular with tourists, claiming 28 lives.
Prime Minister Narendra Modi's office tweeted that Mr Modi was "anguished" over the news of the deaths.
"My prayers and solidarity with those who lost their near and dear ones in the accident", he tweeted.