The bus ended up sliding around 650 feet down a hill.
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Mr Gelal said the bus was overcrowded because of a severe fuel shortage in the country that has limited transportation.
The injured are receiving medical treatment at Dhunche and Trishuli Hospitals.
Police, soldiers and local villagers have helped recover injured people and bodies from the wreckage.
There were a few 70 people aboard a bus from Kathmandu to Chilime, a few traveling on the roof of the vehicle.
Police are investigating the incident.
Nepal usually gets its fuel from India, but the import of fuel and other supplies has been cut off since September due to the blockage of a key border point between the two countries at the hands of ethnic protesters.
The death toll from the passenger bus accident at Ramche VDC-3 in Rasuwa district has reached 34, officials confirmed.
A passenger named Shiva Acharya who escaped the accident by leaping off the bus as it tilted over, said the Nepal bus accident was caused by a flat tire on the front wheel of the bus.
So far, authorities have said “at least” 20 people have died – including one child.
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The accident occurred as the driver lost control and the bus rolled down the hill.
