Cyclone Hudhud is pounding the eastern Indian coast, causing extensive damage and prompting the evacuation of some 300,000 people.
The cyclone, classed "very severe" and bringing winds of up to 195km/h, is expected to make landfall soon near the city of Visakhapatnam.
Hundreds of trees have been uprooted and power lines brought down in Andhra Pradesh and Orissa states.
Two people have so far been reported killed in Andhra Pradesh.
The BBC reports it is feared a storm surge of up to two metres could inundate low-lying areas and hundreds of relief centres have been opened in the two states. Disaster relief teams have also been sent.
The authorities say the next five to six hours will be crucial.
The strength of the cyclone has been revised upwards since Friday, and the Indian Navy is on standby to assist.
The two deaths occurred in separate incidents in Andhra Pradesh's Srikakulam district, the state's disaster management department said.
One was killed by a falling wall and the other by a tree.
The streets of Visakhapatnam, one of the largest cities in south-east India and home to a major naval base, remain largely deserted.
This week's evacuation effort was comparable in scale to the one that preceded Cyclone Phailin exactly a year ago, and which was credited with minimising fatalities to 53. When a huge storm hit the same area 15 years ago, 10,000 people died.