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The extent of the damage is difficult to determine. The area is almost impossible to reach, as the cyclone has torn down bridges and made roads and railways impassable.
All communications have been cut, and the rescue effort is being hampered by the continuing bad weather.
Officials in the state capital, Bhubaneshwar, say nine deaths have been confirmed, but that number is expected to rise rapidly.
Many towns and villages have not been able to report casualty figures or damage assessments because telephone lines have been brought down.
The winds are believed to have reached over 160 mph (250 km/h) - some of the highest ever recorded in the region.
A devastating tidal wave has also driven in across the low-lying plains along the coast, wiping out entire villages.
Unconfirmed reports say the flooding stretches as much as nine miles inland.
Army helicopters have begun dropping food parcels to survivors, and have reported thousands of people stranded on the roofs of their houses or huddled together in pockets of high ground.
The government is to deploy soldiers to help the rescue effort, and emergency specialists are also making their way to the region.
There is serious concern, however, that the scale of the disaster and the remoteness of some of the communities affected will make it extremely difficult to get supplies through to the worst-hit areas.
The longer relief is delayed, the higher the likelihood of water-borne diseases and starvation setting in.
There has already been a call from some politicians in Delhi for the government to call on the international community for help.
It is the second cyclone to hit the area in two weeks.
The first, with winds of about 135 mph (217 km/h), hit a little further down the coast in mid-October.
It killed more than 150 people and affected nearly 500,000 others.
The storm became known as a super-cyclone because of the lethal combination of very high winds and a powerful tidal surge.
It is thought to have killed at least 10,000 people and left an estimated 1.5 million homeless. It was among the worst storms ever to hit India.
Tens of thousands of people were left stranded, the water around them contaminated and awash with corpses.
Many died from starvation and water-borne diseases in the weeks immediately after the cyclone, as the rescue workers could not reach them quickly enough.
Work is still going on to rebuild the devastated communities following the Orissa cyclone, but voluntary organisations working in the area have described the pace of reconstruction as "excruciatingly slow".
The area continues to be at high risk from flooding and other storms.
In 2001, Orissa's worst monsoon floods in 50 years killed nearly 100 people and destroyed hundreds of thousands of houses.
Many of those affected were still living in temporary shelter after the 1999 cyclone.
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