The cyclone, classed “very severe” and bringing winds of up to 120mph, 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.
It is feared a storm surge of up to two meters could inundate low-lying areas and hundreds of relief centers 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 October 10, 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.
K Hymavathi, the special commissioner for disaster management for Andhra Pradesh state, said: “Hundreds of trees have been uprooted and power lines knocked down.”
He added: “The situation is very severe. The national highway in the region has been shut.”
In its latest report, the India Meteorological Department said sea conditions would become “phenomenal” off the north Andhra Pradesh and south Orissa coasts.
It also warned that a storm surge of up to two metres would “inundate low-lying areas of Visakhapatnam, Vijayanagaram and Srikakulam”.
Pradeep Kumar Mohapatra, a special relief commissioner, said that authorities were ready.
“The administration is fully geared,” he said.
“The collectors [senior government officials] have been given total clearance to take up any evacuation wherever necessary for vulnerable areas which are likely to be inundated.”
A super-cyclone in 1999 killed more than 10,000 people in Orissa.
India’s eastern coast and Bangladesh are routinely hit by cyclonic storms between April and November which cause deaths and widespread damage to property.
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