Rivers across the coastal western state of Gujarat have broken their banks and more than 23,000 people have been evacuated from their homes, according to the reports.
The Business Standard newspaper said 15 people had been killed since Monday across eight of the state's districts.
Fishermen have been advised not to venture into the sea, chief minister Bhupendra Patel said in a social media post that fishing crews had been told not to venture into rough seas.
Monsoon rains cause widespread destruction every year, but experts say climate change is shifting weather patterns and increasing the number of extreme weather events.
The northeastern state of Tripura was battered by floods and landslides last week, with more than 20 people killed.
Next door and downriver in Bangladesh, heavy floods killed at least 40 people over the same period with nearly 300,000 residents taking refuge in emergency shelters.
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