Thousands of residents in southeast India headed back home on Friday, two days after being evacuated as a cyclone struck killing 10 people, with two members of a tanker crew still missing.

The oil tanker "Pratibha Cauvery" remained stranded in shallow water close to the city of Chennai as shipping authorities drew up a plan to refloat the vessel.

The bodies of three of the tanker's crew were found after they drowned when their lifeboat capsized in rough seas as they tried to reach shore during Cyclone Nilam.

"We have found the bodies of three sailors in the sea but two others are still missing. Search operations continue," Srikanth, a spokesman for the Indian Coast Guard who only uses one name, told AFP.

About 5,000 people who were forced to flee from coastal towns to seek shelter in schools and government buildings have started to return to their houses and a ban on fishermen putting out to sea was lifted.

"We have hired 400 trucks to transport families from rescue shelters to their houses. They have all been given food packets and medicines," Jayraman, a disaster management official in Chennai, said.

A team of experts from Singapore assessed damage caused to the "Pratibha Cauvery".

"The experts will be diving to check the bottom of the ship and investigate after the cyclone," Atulya Mishra, an official at the Chennai Port Trust said, adding that the ship was not carrying oil.

"We will refloat the ship after their report," he added.

Cyclone Nilam struck the historic port of Mahabalipuram, 50 kilometres (30 miles) south of Chennai on Wednesday evening before moving inland.

The last deadly cyclone in India struck in the same southeast region in January, claiming 42 lives and leaving a trail of destruction across Tamil Nadu state.