Almost 500,000 people have been evacuated from the path of Cyclone Phailin in Orissa state and neighboring Andhra Pradesh.
The massive storm made landfall on Saturday, packing winds of up to 125 mph.
Five deaths have so far been linked to the cyclone.
In 1999 a cyclone killed more than 10,000 people in Orissa, although authorities say they are better prepared this time.
At daybreak on Sunday there was an anxious wait to see the extent of the damage.
Communications are down in many areas with road and rail links closed, making an assessment even more difficult.
The Times of India reported that a storm surge more than 9 ft high had inundated areas of Ganjam, Khurda, Puri and Jagatsinghpur districts of Orissa and the Srikakulam district of Andhra Pradesh.
In the Orissa state capital of Bhubaneshwar, government workers and volunteers were assembling hundreds of thousands of food packages for relief camps.
Bhubaneswar shop owner Susil Kumar Singh was one of only a few traders keeping his store open.
“Everyone’s in trouble so I’ve kept my shop open to help them,” he told AFP news agency.
“Right now, there’s no drinking water and trees are falling down all around.”
Orissa Chief Minister Naveen Patnaik appealed for calm.
“I request everyone to not panic,” he said.
“Please assist the government. Everyone from the villages to the state headquarters has been put on alert.”
The Indian Army’s National Disaster Response Force (NDRF) said 1,200 troops had been sent to Orissa and 500 to Andhra Pradesh.
“As soon as the fury of the cyclone abates our boys will start their work,” NDRF director general Krishna Chaudhary told reporters.
“The teams have medical first responders (for first aid) and heavy cutting equipment. In the case of cyclones there is a likelihood of collapsed buildings.”
Up to 10in of rain is predicted for Orissa and the north coast of Andhra Pradesh throughout Sunday and Monday, forecasters said.
In the coastal town of Gopalpur, hundreds of terrified residents spent the night huddled in shelters, schools and public buildings.
Witnesses reported seeing shards of glass and asbestos sheets flying through the air as the cyclone struck.
Store signs and other debris were being pitched high in the air by storm gusts and elaborate decorations for a major Hindu festival were strewn over the main road.
Officials had earlier said that no-one would be allowed to stay in mud and thatched houses along the coast of Orissa and Andhra Pradesh states, but some residents said they wanted to stay put.
“Many people refused to move, had to be convinced, and at times the police had to forcefully move them to safe places,” said Home Minister Sushilkumar Shinde.
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