It was noted that as a result around 30 people, 27 of them were children, died.
Most of the students were aged between 10 and 12 years and hailed from a local school, he added.
Investigators say tire marks at the accident site suggest that the bus was traveling too fast and the driver may have made a mistake in steering the wheel.
Eyewitnesses said the vehicle skidded as it turned a corner and left the mountainous road, India's ANI news agency reported.
The 42-seater bus was on its way to drop students to their homes when it plunged off the mountain road and into the gorge.
GETTYThe bus fatal plunge occurred at about 3pm local time
Rescue work has been initiated and those injured are being admitted in nearby hospitals, said Sandeep Kumar, the deputy commissioner of Kangra district. Also killed two teachers and the bus driver. Transport Minister Govind Thakur and all the other members of the state Cabinet have condoled the death of school children. "Thoughts and prayers with the bereaved families and with those injured", said Kovind in a statement posted on Twitter.
Chief Minister Jai Ram Thakur said that the food and civil supplies minister had been sent to the spot. Modi tweeted from his official account, "I am deeply anguished by the loss of lives due to a bus accident in Kangra, Himachal Pradesh".
The state government has announced 500,000 rupees ($7,700) in compensation for each victim's family.
Search and rescue operations are over and 11 children were taken to two hospitals.