The rain claimed the life of a eight-year-old girl, who was crushed to death when a portion of her hut collapsed early on Tuesday.
The Supreme Court also asked the supervisory committee to decide on Tamil Nadu's plea in ten days from Monday.
The emotional appeal and sane advise came from the bench when Tamil Nadu brought to the notice of the court that the Karnataka chief minister has said that not a drop of water will be released to it.
Karnataka and Tamil Nadu on Monday sparred at the meeting of Cauvery supervisory committee in New Delhi over the latter's share of the Cauvery water.
The Supreme Court on Tuesday refused to give an urgent hearing to a plea of the Tamil Nadu government for setting up the Cauvery management board for implementation of the Cauvery water disputes tribunal award, saying there is "no urgency" for it.
Modi assured to extend all required assistance to the state to face the situation, the Chief Minister's office said.