The storm in the Bay of Bengal intensified into a cyclone on Sunday, packing wind speed of more than 75 kmph, and is expected to get stronger, the weather office said.
However, it is expected to fizzle out next week without making a landfall.
Under the influence of the cyclone, northern Andhra Pradesh and Odisha coasts are expected to experience heavy winds and rains from Tuesday, the weather office said.
The cyclonic storm 'Asani', Sinhanlese for 'wrath', lay centred over southeast Bay of Bengal 380 km west of Port Blair in the Andaman Islands at 5:30 am on Sunday, the weather office said.
It is very likely to move northwestwards and intensify further into a Severe Cyclonic Storm over east central Bay of Bengal during the next 24 hours, the India Meteorological Department (IMD) said in a bulletin issued at 8:30 am.
According to the track of the cyclone forecast by IMD, the cyclone was very likely to continue to move northwestwards till May 10 evening and reach West central and adjoining Northwest Bay of Bengal off North Andhra Pradesh and Odisha coasts.
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Thereafter, it is very likely to recurve north-northeastwards and move towards Northwest Bay of Bengal off Odisha coast, it said.
According to the cyclone trackers, the weather system is expected to be at its strongest, packing wind speed of 60 knots (111 km per hour), on Monday with its fury on full display in the Bay of Bengal.
The severe cyclonic storm is expected to start weakening gradually from Tuesday as it moves towards the coasts of northern Andhra Pradesh and Odisha.
Coastal districts of Odisha and the southern part of West Bengal, including the state capital Kolkata, are likely to be lashed by light to moderate rain from Tuesday, the IMD said.
Fishermen have been advised not to venture into the sea and along and off West Bengal and Odisha coasts from May 10 till further notice.
The sea conditions near the Odisha coast will become rough on May 9 and rougher on May 10. The wind speed in the sea will increase to 80-90 kmph on May 10.