The bus with Indian number plate was carrying around 45 pilgrims from Gujarat who were returning to Gorakhpur in India after a pilgrimage to Pashupatinath Temple in Kathmandu, Superintendent of Police Bishworaj Pokharel said.
Twelve passengers - six men and six women - died on the spot. Two others succumbed to their injuries shortly after being taken to hospital.
The injured passengers have been rushed to Kathmandu for medical treatment. The condition of four of them are critical.
The embassy has deputed a team comprising Consular Wing officials to the accident site to better coordinate the rescue efforts, the embassy said in a statement.
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Rescue efforts are going on at the accident site, which lies along the Tribhuvan Highway, with the help of security personnel and the local people, he said.
The death toll might rise as the bus was trapped in a gorge like site and some passenger might have been trapped under the bus, Pokharel said.
The famous 5th century Pashupatinath temple is dedicated to a manifestation of Shiva called Pashupati (Lord of Animals). It attracts thousands of pilgrims each year, mostly from India.