Most deaths have taken place in the southern states of Telangana and Andhra Pradesh, where more than 140 people have died since Saturday.
Allahabad in Uttar Pradesh recorded 48C while temperatures rose to above 44C (111F) in the capital, Delhi.
Authorities have urged people to stay indoors and drink plenty of fluids.
Heatwave conditions have been prevailing in the two worst-affected southern Indian states since mid-April, but most of the deaths have happened over the last week.
The worst-hit state has been Andhra Pradesh where 246 people have died from the high temperatures in the last week, most of them in the last few days.
“The majority of the victims are people who have been exposed to the sun directly, usually aged 50 and above and from the working classes,” news agency AFP quoted P Tulsi Rani, special commissioner of Andhra Pradesh’s disaster management department, as saying.
“We are asking them to take precautions like using an umbrella, using a cap, taking a huge quantity of liquids like water and buttermilk, and wearing cotton clothing,” he added.
The Press Trust of India news agency said the heatwave had killed 186 people in 10 districts in neighbouring Telangana state, with 58 people dying since Saturday.
The meteorological department said the sweltering conditions were likely to continue for a few more days.
“No relief” is expected in Andhra Pradesh, Telangana, Delhi and other northern states for the next four days, and the “heatwave will continue,” an official said.
Reports said at least 10 people had died of the heat in the eastern state of West Bengal.
Non air-conditioned taxis will be taken off the road for five hours during the day in the main city in the state capital, Kolkata, after two drivers died from heat stroke.
Meteorological officials said the heatwave was due to a lack of rain.