A cyclone packing winds of up to 150 kilometres per hour and heavy rains hit eastern India early on Thursday, with over 300,000 people evacuated from low-lying areas and two men reported killed.

Officials in neighbouring Bangladesh said they were on alert in the coastal district of Cox's Bazar, home to around one million Rohingya refugees from Myanmar living in tarpaulin and bamboo shelters.

Cyclone Titli, which intensified into a “very severe cyclonic storm” over the Bay of Bengal, made landfall on India's eastern coast early on Thursday, the Press Trust of India (PTI) news agency reported.

Wind speeds of up to 150 kilometres per hour were reported, with gusts of up to 165 kph.

One man died in a house collapse while another was killed by a falling tree, an emergency services official was quoted as saying by PTI.

The Odisha state government evacuated more than 300,000 people from five coastal districts on Wednesday while local schools, colleges and childcare centres were ordered closed and fishermen advised not to go out to sea.

“We have already evacuated three lakh (300,000) people and more may be shifted to safer places in view of the very severe cyclone,” PTI quoted Chief Minister Naveen Patnaik as saying.

They were accommodated in more than 1,100 cyclone shelters. Officials have also shifted 123 pregnant women to hospitals.

Trees and electricity poles were uprooted, officials told PTI, with roads and houses also damaged.

The Bangladeshi government's Rohingya commissioner Mohammad Abul Kalam said the cyclone had brought rain to Cox's Bazar over the last three days.

“We're on alert. We've taken adequate cautionary measures for the cyclone,” Kalam told AFP, adding Dhaka had held meetings with agencies operating in the camps in preparation for the storm.