The strongest cyclone to hit India in five years killed at least 33 people in the country's eastern Odisha state before swinging north-eastwards into Bangladesh, where five more people died.

Key points: Two children were among those reported killed in India

Two children were among those reported killed in India The destruction in the town of Puri was said to be "unimaginable"

The destruction in the town of Puri was said to be "unimaginable" Mass evacuations in India and Bangladesh are credited with saving many lives

But the evacuation of millions of people across the two countries is believed to have saved many more lives.

Tropical Cyclone Fani, which made landfall early on Friday, lost some of its power and was downgraded to a depression as the storm hovered over Bangladesh.

This satellite image shows Cyclone Fani in the Bay of Bengal. ( AP: Indian Metrological Department )

"The fear of a major disaster is mostly over as [Fani] has weakened," said Shamsuddin Ahmed, director of the Bangladesh Meteorological Department.

A storm surge still breached embankments to submerge dozens of villages on Bangladesh's low-lying coast, a disaster ministry official in Dhaka said.

The storm also 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 said.

In all at least five people were killed, 63 injured, and more than the 1,000 houses had been damaged, Bangladeshi authorities said.

Indian media reported that most deaths have been caused by falling trees.

Trees lie uprooted after Cyclone Fani made landfall in India, where officials evacuated 1.2 million people from the storm's path. ( AP )

The seaside temple town of Puri, which lay directly in the path of Fani, suffered extensive damage as winds gusting up to 200 kph tore off tin roofs, snapped power lines, and uprooted trees.

"The cyclone has killed 21 people in Puri and about 300 people are injured," Brajabandhu Dash, medical officer at Puri, told Reuters.

"Destruction is unimaginable … Puri is devastated," Odisha's Special Relief Commissioner Bishnupada Sethi said.

Video footage taken from an Indian navy aircraft showed extensive flooding in areas around Puri, with wide swathes of land submerged in the aftermath of the storm.

1.2 million evacuated in 24 hours

Evacuees are beginning to return to badly damaged towns in India and Bangladesh. ( AP )

According to preliminary reports, Cyclone Fani damaged power infrastructure worth more than 12 billion rupees ($247.2 million) and authorities are trying to restore electricity supply for emergency services.

More than 60,000 people including officials and volunteers were involved in relief operations, said special relief commissioner Bishnupada Sethi, who monitored the evacuation.

The relief effort used sirens, loudspeakers and sent more than 20 million mobile messages to the targeted people, he said.

The cyclone season in the Bay of Bengal can last from April to December. In 1999, a super-cyclone battered the coast of Odisha for 30 hours, killing 10,000 people.

Since then, technological advances have helped weather forecasters track the cyclones more accurately, giving authorities more time to prepare.

This time, as Cyclone Fani approached, Odisha moved 1.2 million people to safety in 24 hours, which Mr Patnaik described as "one of the biggest human evacuations in history".

"Instead of it being a tragedy of humongous proportions, we are in the process of restoring critical infrastructure," he said.

About 1.2 million people living in the most vulnerable districts in Bangladesh had also been moved to some 4,000 shelters.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 34 seconds 34 s Cyclone Fani lashes coastal areas of eastern India.

Reuters