The minibus, which was on its way from Keshwan to Kishtwar, skidded off the Keshwan-Thakrai road and rolled down into the deep gorge around 7.30 am, officials said.
The DC of Kishtwar Angrez Singh Rana, confirmed the death toll at 35. Those injured will have been airlifted to GMC Hospital in Jammu.
Prime Minister Narendra Modi condoled the deaths and said the incident was "heart-wrenching". "The accident in Jammu and Kashmir's Kishtwar is heart-wrenching. We mourn all those who lost their lives and express condolences to the bereaved families. May the injured recover at the earliest," he tweeted.
The bus, which was on its way to Kishtwar from Keshwan, skidded off the road at Sirgwari and rolled down into the gorge at around 7:30 am.
Earlier, police officials had said that 24 people have been killed in the accident.
The injured have been taken to District hospital in Kistwar.
The local residents were the first respondents when the accident took place.
Overloading, over-speeding and dilapidated road conditions have caused tragic accidents in the hills of Doda, Kishtwar, Rajouri and Poonch districts in the past as well.
On June 27, 11 students of a private computer training institute were killed in a tragic accident in Pir Ki Gali area of the Mughal Road that connects the Rajouri-Poonch districts in the Jammu division.
Following this accident, authorities in Poonch district have banned all excursions by educational institutions unless specifically allowed by the district administration.
(Further details are awaited)