Large areas of India are scorched and dry
He said 373 deaths had so far been confirmed. Unofficial figures put casualties above 500.
Many of the deaths in Andhra Pradesh, where temperatures have soared on occasion to a blistering 49C, have been among elderly street vendors overcome by heatstroke and dehydration.
The Andhra Pradesh government has advised people to stay indoors and drink plenty of water until cooler weather arrives - probably in three or four days.
Mr Naidu said his government would provide 50,000 rupees to the family of every victim.
Meteorologists say the heatwave is caused by winds blowing from deserts in north-western India.
Monsoons
There have also been deaths in other states and in Pakistan.
In north-west India, Punjab and Haryana states, as well as the federal capital, Delhi, have all seen very high temperatures, but no deaths have been reported there.
Indian weathermen say the heat wave is expected to recede once the monsoon rains arrive in early June.
'Poor suffer'
This is not the first time that large parts of India have reeled under oppressively high temperatures.
CVV Bhadram, Director of Meteorology in Hyderabad, says a May heatwave is not surprising.
"But what is unusual this time is the intensity and the persistence for over a week," he says.
The administrator of worst-hit Guntur district in Andhra Pradesh, where the official death toll has reached 84, says elderly people and the young are particularly vulnerable.
But social activists like Gayathri Ramachandran see these deaths as part of an economic problem.
"Usually it is the people forced to work in this harsh weather who suffer sun strokes and other heat related problems," she says.
"Undernourishment is also a problem."