Northeast India has also been hit by floods with 11 deaths recorded as rivers burst their banks.
A statement by the Home Ministry said that 47 people have died, while 29 are now missing following monsoon rainfall that continued to impact the mountainous areas of the country since Thursday.
Some 1.9 million people have been affected by the floods in Bihar, state officials said.
Three rivers are overflowing in northeastern India and submerging parts of the region.
Almost 80% of Assam's Kaziranga National Park, home to the endangered one-horn rhinoceros, has been flooded by the mighty Brahmaputra river, which flows along the sanctuary, forest officer Jutika Borah said.More news: Barry likely to weaken further by Monday evening: NHC
Boats near a submerged house in Burha Burhi village east of Gauhati India.
Since early July, flooding and landslides have damaged thousands of shelters at the refugee camps, killing two people, including a child, Human Rights Watch said in a release last week.
The monsoon rains began on Thursday, inundating low-lying towns and villages, with tens of thousands evacuated after major rivers swelled to risky levels, according to the Nepalese Ministry of Home Affairs.
The National Emergency Operation Center said 14 highways across the nation were blocked by floods or mudslides and attempts were being made to clear the debris and open them for traffic.More news: Clarke stakes Grizzlies to summer league crown
Nepal's Department of Hydrology and Meteorology warned of more troubles ahead in a flood warning for the southern region near the main rivers, urging people to keep watch on rising water levels and move to higher grounds when needed.
Building collapses are common in India during the June-September monsoon season, when heavy rains weaken the foundations of structures that are poorly constructed.
"The flood situation has turned very critical with 31 of the 32 districts affected", Assam Chief Minister Sarbananda Sonowal told reporters.
An Indian woman shifts her belongings on a flooded road.More news: Christoph Waltz To Reprise His Role In ‘Bond 25’
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