The worst-hit area is the southeastern state of Andhra Pradesh, where authorities say 852 people have died in the heat wave. Another 266 have died in the neighboring state of Telangana.
India recorded its highest maximum temperature of 47 degrees Celsius -- 117 degrees Fahrenheit -- at Angul in the state of Odisha on Monday, according to B.P. Yadav, director of the India Meteorological Department.
Hot, dry conditions are being made worse by winds blowing in from Pakistan's Sindh province across the northern and central plains of India. "This extreme, dry heat is being blown into India by westerly winds," Yadav said.
The high temperatures are expected to continue for another two days before any respite, the meteorological department warned Tuesday. However, the agency said that another hot spell would likely soon follow.
Among the worst-hit states are Andhra Pradesh and Telangana in the south. The northern states of Rajasthan and Haryana are also reeling from the intense summer as is India's capital, New Delhi, Yadav said.
Heat taking toll on the poor
Many of the dead are reported to be poorer people, beggars and the homeless as well as construction workers who are expected to work on building sites in direct sunlight.
Only two-thirds of the country's 1.2 billion people have reliable access to electricity, meaning millions are enduring the blistering heat without relief.
For those who do have electricity, power has dipped in and out as extra demand to run fans and air conditioning has put pressure on the system, said CNN Mumbai correspondent Mallika Kapur.
Many people without ways to cool their homes are seeking shelter in shops and malls -- anything to escape the heat, she said.
Temperatures have been at a sustained high over the past few days, with little change even at night, and are expected to remain high for days, CNN meteorologist Tom Sater said.
India's monsoons will provide some relief, but the rains are projected to arrive in one more week. Once they hit India's southeastern coastline, they will likely take a few more weeks to reach the drier northern parts of the country.
State authorities have been advising people to stay indoors and drink water.
Experts say that hot conditions should not usually lead to this many fatalities. But many of the affected areas in India are humid, which worsens the level of stress caused by excessive heat.
Heat waves are not uncommon in India. Studies suggest
they are likely to get more intense and more frequent.