Dozens of people have been killed and nearly three million hit by floods triggered by torrential monsoon rains in India and Nepal, officials said on Saturday.

At least 38 people have died in heavy flooding and landslides across the region, where homes have been swept away and crops destroyed.

In Nepal, officials said 11 people had died this week in floods and landslides.

They said thousands of others were hit by the flooding, which disrupted road transport and shut down schools and markets in towns and villages in rain-lashed southern plains.

"Dozens of houses have been swept away and the crops damaged," said district administrator Durga Prasad Bhandari from the town of Gaur, southwest of the capital Kathmandu.

Swirling floods in the eastern Indian state of Bihar, which adjoins Nepal, swept away 14 people and wreaked havoc, said officials.

Two million people were affected by the floods, which inundated homes and farms in India's second most populous state, they said.

Twelve people were killed in worst-hit Bhagalpur district, while two people drowned elsewhere in the state, the Press Trust of India quoted relief officials as saying.

The overnight deaths took India's rain-related toll to almost 800 since the onset of the monsoon in June, according to figures compiled from officials and media reports.

Authorities in Assam and Meghalaya appealed for help from the military after landslips and flash floods killed 13 more people and displaced around 750,000 people in the two adjoining states.

A spokesman for the Assam state government said nine people died when large boulders crashed into a rain-swept settlement. Four people drowned overnight in separate incidents, he said.

Food, water and medicines were being distributed to the affected people, Dhemaji district magistrate D.N. Mishra said by telephone.

Assam water resources minister Bharat Narah said preventive measures, including the strengthening of dykes and embankments, were being taken.

Overflowing rivers also burst their banks in India's West Bengal state, which borders Assam. The flood waters submerged homes and an under-construction hydro-power station, officials in state capital Kolkata said.