At least 16 people have been killed this week in heavy monsoon rains that have lashed western India, including the desert state of Rajasthan, with more than 24,000 villagers evacuated to higher ground, officials said on Tuesday.

Hundreds of rescuers using motor boats saved 789 people, including some pregnant women, from being swept away by the swirling floodwaters in six districts in Gujarat state, said Ranvijay Singh, a government official.

The rescuers found six bodies in flooded villages on Monday and Tuesday, raising the death toll in Gujarat to 70 since the start of the monsoon season, which runs from June through September.

Mount Abu, a popular hill station in Rajasthan, received 80 centimetres of rain on Monday, surpassing a 1992 record of 66 centimetres of rain in a 24-hour period, according to the state flood relief department.

At least 10 people have died in the past two days due to drowning and house collapses in Rajasthan, where air force helicopters evacuated 450 people from inundated areas in Jalore, Pali and Sirohi districts, the flood relief department said.

At least 60 people have died in northeastern Assam state due to flooding since the start of the monsoon season in June.

Another 14 people died in the nearby state of Arunachal Pradesh last month after a mudslide swept through a village.