Most deaths have taken place in the southern states of Telangana and Andhra Pradesh, where at least 1,118 people have died since last week. Reports say at least 24 people have died from the heat in West Bengal and Orissa. Temperatures are likely to drop in some parts over the coming days.
Hospitals are on alert to treat heatstroke patients and authorities have advised people to stay indoors.
Heatwave conditions have been prevailing in the two worst-affected southern Indian states since mid-April, but most of the deaths have happened in the past week.
In the worst-hit state of Andhra Pradesh, where temperatures climbed to 47C on Monday, 852 people have died.
"The state government has taken up education programmes through television and other media to tell people not to venture into the outside without a cap, to drink water and other measures," news agency AFP quoted P Tulsi Rani, special commissioner for disaster management in the state, as saying.
"We have also requested NGOs and government organisations to open up drinking water camps so that water will be readily available for all the people in the towns," he added.
In neighbouring Telangana state, 266 people have died in the last week as temperatures hit 48C (118F) over the weekend.
Temperatures fell slightly in Telangana on Tuesday, and are expected to start dropping in Andhra Pradesh by the end of the week.
The weather is likely to cool further when the summer monsoon begins at the end of the month. (BBC)