Superintendent of Police Santosh Patyal confirmed the deaths. All the dead students were below the age of 10. The bus driver and two teachers were among the dead.
The death toll could rise as some students were still trapped in the mangled bus even as the rescue operation is on, police added.
Local villagers had begun rescue operation even before officials could reach the spot, eyewitnesses said.
Around 45 students of Wazir Ram Singh Pathania Memorial Public School were returning home when the bus skidded off road and fell into the 100-feet deep gorge near Gurchal village on the Nurpur-Chamba road, some 300 km from the state capital.
Teams of local administration and the National Disaster Response Force were involved in the rescue and faced tough time in pulling out the victims from the mangled bus.
Some of the injured were referred to hospitals in Pathankot in Punjab.
Chief Minister Jai Ram Thakur condoled the deaths.
A magisterial inquiry has been ordered.