The Kathmandu-bound bus from Rajbiraj fell into the Trishuli River while negotiating a turn at Ghatabesi, 70-km west of the capital, around 5:00 am, said Superintendent of Police, Dhading, Dhruba Raj Raut.
Security personnel, including those from the Nepal Army and Armed Police Force, rescued 16 injured passengers who had fallen into the river along the Prithvi Highway.
Raut put the death toll at 31 and authorities said the toll could rise further.
The rescue teams have pulled out 28 dead bodies so far and the search was on for other missing passengers.
According to the police, most of the deceased were from Saptari district and 12 of them have been identified.
An Indian woman, Mamata Devi Thakur, also died in the accident, police said.
All injured passengers were taken to nearby hospitals, but two of them who suffered serious injuries were rushed to Kathmandu for treatment, according to the police.
According to preliminary reports, the accident occurred because the driver failed to take the high speed bus under control at the turning point due to poorly visibility.
Altogether 52 passengers were travelling on the bus, police said.
While the police prima facie blamed visibility for the accident, such mishaps are not uncommon in the Himalayan nation and occur mostly due to poor infrastructure and reckless driving.
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