At least 12 people, including six children, have drowned in torrential rain in Sri Lanka caused by a slow-moving storm now headed toward India.

More than 335,000 people in Sri Lanka have been forced to flee after their homes were flooded in the storm, Colombo's Disaster Management Centre (DMC) said.

It said two men driving a tractor and trailer which had been transporting six children in the eastern Amara district when it was swept away in floods.

The men had been reported as missing and search efforts were underway.

Indian weather officials said there was a "possibility" that the deep depression over the southwest Bay of Bengal could develop into a cyclonic storm.

Cyclones are common and often deadly in the region.

Having skirted the coast of Sri Lanka, the storm was headed north towards India's southern Tamil Nadu state.

The India Meteorological Department said the storm was expected to hit Tamil Nadu and Puducherry city's coastline on Saturday morning as a "deep depression" with winds "gusting up to 70 kph".

Sri Lanka's DMC said some 335,155 people were seeking temporary shelter in public buildings after their homes were swamped.

Nearly 100 homes had been completely destroyed while another 1,700 had been badly damaged due to rains as well as mudslides.

The government said it deployed over 2,700 military personnel to help in relief operations.

Deadly rain-related floods and landslides are common across South Asia, but experts say climate change is increasing their frequency and severity.

AFP/ABC