Floods caused by heavy monsoon rains in two of India's poorest states have displaced or affected 8 million people and killed 111 since May, authorities said on Tuesday, at a time when coronavirus cases have swelled there.

The Brahmaputra river in Assam is flowing above the "danger level" in many places, while heavy rains that began this week in Bihar in the east will last until Wednesday, officials say.

Since the start of the monsoon season on June 1, Assam has received 15 per cent more rainfall than a 50-year average and Bihar 47 per cent more, according to the weather department.

The floods in Assam, where at least nine one-horned rhinos have drowned in an inundated national park, have so far affected 5.7 million people, more than 45,000 of whom are still sheltered in makeshift relief centres.

In Bihar, floods have stranded more than 2.4 million people, with around 12,800 staying in government shelters, complicating efforts by officials to enforce social distancing measures to halt the spread of the novel coronavirus in the state.

It has so far reported more than 41,000 infections, with 255 deaths from the Covid-19 disease, straining health resources in the state.

"The number of Covid-19 patients in Bihar is higher than expected," Naveen Chandra Prasad, the state's director-in-chief of public health, told Reuters. "Floods and Covid-19 are a combined problem for us."

Assam, meanwhile, is preparing for a peak in coronavirus infections in mid-September. It has so far reported more than 33,500 cases, with 86 deaths.