The incident took place as the bus with 85 passengers, heading for Kattike Deurali from Kathmandu, skidded off the road at Birta Deurali-7 in Kavre.
According to the District Police Office Kavre, 33 people were killed in the accident.
As many as 43 others have been injured in the incident, police said.
A Nepal Army helicopter airlifted 15 injured passengers to Kathmandu for treatment, according to the Ministry of Foreign Affairs.
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Prime Minister Prachanda directed concerned stakeholders including the government bodies to intensify rescue mission.
Nepal has many mountainous areas and most roads are narrow.
Most accidents in Nepal are blamed on poorly maintained vehicles and road conditions. Buses are crowded and people also travel on the roofs of buses.