The water resources ministry asked authorities in Andhra Pradesh, Tamil Nadu and Odisha to ensure "sufficient vigil" in coastal areas for the next three days as the path of a depression developing in the Bay of Bengal "is not yet well- established".
According to the advisory, the rivers in North Konkan, north-central Maharashtra and Gujarat are likely to rise rapidly.
"Rivers in the Godavari basin in North Madhya Maharashtra in Nasik district are likely to rise ... as the rainfall is likely to affect only a very small catchment area of this basin ... not much effect will be felt in the Godavari and its tributaries," it read.
"As the rainfall will be only for one day, no major flooding is expected in the basin," the ministry added.
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The Mahi river in Gujarat may rise in view of heavy rain in Mahisagar, Panchmahal, Kheda and Vadodara.
The water level in the Sabarmati may increase in areas which are directly in the path of the cyclone "which would have weakened sufficiently by the time it reaches this basin", according to the advisory.
Rivers Rishikulya, Vamsadhara and Nagavali in south Odisha and north Andhra Pradesh are likely to surge due to heavy rain expected over the next two days.
The ministry said rain in south Odisha and north coastal Andhra Pradesh may lead to an increase in the water level of the Sabari basin in Nowrangpur, Malkangiri, Koraput and East Godavari districts.
The Krishna river and its tributaries may get inflows in view of rainfall in Krishna and Guntur districts of Andhra Pradesh.