The weather phenomenon will cause heavy rainfall and high-velocity wind in coastal districts of Odisha, West Bengal and Andaman and Nicobar. It is likely to make landfall on the West Bengal coast on May 20.
The National Disaster Response Force has sent 10 teams to Odisha and seven to West Bengal to tackle the impending cyclone.
"The severe cyclonic storm 'Amphan' over central parts of South Bay of Bengal and neighbourhood moved slowly northwards with speed of five kmph during past six hours. Further intensified into a very severe cyclonic storm," said IMD scientist R.K. Jenamani.
The cyclone currently lies centred at about 960 km south of Odisha's Paradip, 1110 km south-southwest of West bengal's Digha and 1,230 km south-southwest of Bangladesh's Khepupara.
It is very likely to intensify further into an extremely severe cyclonic storm during the next 24 hours.
According to the weather department, the cyclone is also very likely to move nearly northwards slowly during next 12 hours and then re-curve north by northeastwards and move fast across northwest Bay of Bengal and cross West Bengal and Bangladesh coasts between Digha and Hatiya islands on May 20.
The weather agency said there can be light to moderate rainfall in Andaman and Nicobar in the next 24 hours. Coastal districts of West Bengal are also likely to experience light to moderate rainfall at many places with heavy rainfall at isolated places on May 19.