With effects felt as far away as Mount Everest, winds gusting up to 200 km per hour sent coconut trees flying and cut off power, water and telecommunications. It destroyed several houses in the Noakhali district, where a two-year-old child and a 12-year-old girl were killed, and about 30 people were injured, local official Tanmoy Das told Reuters.
While not confirming any deaths, Odisha disaster management official Prabhat Mahapatra told AFP there were about 160 people injured in the Hindu pilgrimage city of Puri alone.
At least a dozen people were killed in Bangladesh as the cyclone hovered over the country's southwestern coast, delivering battering rain storms.
Cyclone Fani ("Snake" in Bengali) slammed into the eastern state of Odisha earlier in the day, reportedly killing at least eight people and one in Bangladesh, where it was headed after Kolkata, officials said.
A 250-foot crane crashed onto a building in the coastal state of Odisha, reported NDTV.
In February the International Federation of Red Cross and Red Crescent Societies (IFRC) began distributing tarpaulins ahead of the region's "cyclone season" - but warned that if a deadly storm rolls in, shelters made of battered bamboo and shredded plastic would offer little protection.
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Footage taken from an Indian navy aircraft showed extensive inundation in areas around Puri, with wide swathes of land submerged. Patnaik, while briefing media after the meeting, said over 12 lakh people had been evacuated in 24 hours to safer locations in the state.
It hit the coast of Odisha state on Friday morning, bringing wind gusts of up to 205 kilometers (127 miles) per hour.
Prime Minister Narendra Modi, hoping to be re-elected in India's ongoing election, tweeted that on Monday he would visit Odisha, the state's 46 million people among India's poorest and the worst affected.
According to state Chief Secretary A.P. Padhi, 21 of the 29 deaths were registered in the pilgrim town of Puri, where the storm made a landfall on May 3, flattening fragile houses, uprooting scores of trees, electric poles and mobile towers.
Just about the only good news amid the gloom all around is that flights to and from Bhubaneswar airport resumed operations on Saturday, while train services will be restored, though only partially, today. The storm later weakened and entered West Bengal on Saturday night, after which it moved to coastal areas of Bangladesh.
A 1999 "super" cyclone killed around 10,000 people and devastated large parts of Odisha.
On Saturday Fani was expected in West Bangal's capital Kolkata, a city home to 4.5 million people.