Chief District Officer of Chitwan, Indradev Yadav, confirmed the incident.
According to Yadav, the Kathmandu-bound Angel bus and Ganpati Deluxe, en route to Gaur from the Capital, met with the accident at around 3:30 am.
Twenty-four people were onboard the bus travelling to Kathmandu and 41 on the bus travelling to Gaur, police said.
Three of the passengers on the Ganpati Deluxe bus managed to escape after jumping out of the vehicle, The Kathmandu Post reported.
Details have been received of 21 passengers travelling from Birgunj to Kathmandu on Angel Deluxe. According to the latest information, police have said that there were seven Indian nationals among the passengers on the bus, myRepublica reported.
Yadav said that the rescue workers have started clearing the landslide debris. Expressing grief over the disappearance of the bus in the Trishuli River, Prime Minister Pushpa Kamal Dahal 'Prachanda' has issued directives for immediate search and rescue operations.
"I am deeply saddened by the loss of nearly five dozen passengers and the loss of property due to floods and landslides in different parts of the country when a bus was washed away by a landslide on the Narayangadh-Muglin road section. I direct all agencies of the government, including the home administration, to search and effectively rescue the passengers," Prachanda posted on X.
The prime minister also expressed grief over the loss of life and property due to floods and landslides in different parts of the country. He urged citizens to take necessary precautions.
Nepal Police and Armed Police Force personnel are heading towards the incident sites for rescue operations, Superintendent of Police Bhawesh Rimal said.
Debris from landslides at various places has obstructed traffic on the Narayanghat-Mugling road section.
Meanwhile, in a separate incident, at least 11 people died in landslides and floods triggered by incessant rain in Kaski district on Thursday.
More than 1,800 people have lost their lives in a decade due to monsoon disasters. During this period, about 400 people went missing and more than 1,500 people were injured in the disaster.