Troops rushed to the area to assist with search and rescue operations but they were called off overnight and were to resume at daybreak on Wednesday.
But hopes of finding more survivors in the treacherous mountain river were slim, said Anil Kumar Pandey, the chief district officer.
Ghanashyam Chaudhary, a local police officer, said "hundreds of people went missing" and many may have been swept downstream into remote areas.
As many as 100 people reportedly managed to swim to safety, he added.
Slow rescue
Pandey said helicopters had been requested to help scour the river.
The 500-m long bridge was crowded with pilgrims headed to a religious ceremony to celebrate the full moon that began on Monday, Pandey said.
"The remoteness of the area and poor communication facilities have delayed rescue efforts," he added.
The Himalayan nation is cut by dozens of rivers across one of the steepest topographies in the world.