Dramatic images of the impact of flood water on urban life have been coming out of the affected areas.
Railway traffic, vehicular movement, healthcare services, schools and power supply have been disrupted in both states, officials said.
An Uttar Pradesh government report said 93 people have died since Thursday.
The death toll in Bihar is 29, according to the state disaster management authority. The impact on its main city, Patna, has been grabbing headlines.
People are navigating the main roads - which are dotted with abandoned and partially submerged vehicles - by boat.
A video of a man struggling to pull his cycle-rickshaw out of flood water has been circulated widely on social media.
The city has been deluged with rain since Friday, submerging many residential areas.
The PTI news agency quoted an official as saying that the amount of rain the city received was "completely unexpected".
The state government has asked the Indian Air Force for helicopters and machines to pump out water.
Similar scenes have been reported from neighbouring Uttar Pradesh as well.
"The condition of the water is very bad - the condition of Varanasi is very bad. Drainage arrangements have gone very bad," one local in the northern city of Varanasi told Reuters news.