Supreme Court on Monday said it can consider directing Karnataka to release 20-25 thousand million cubic feet (TMC) water to Tamil Nadu from Cauvery river based on a precedent.
The court was hearing Tamil Nadu´s petition for immediate release of water from River Cauvery from Karnataka.
The two sides exchanged charges during an hour-long hearing and refused to come to any agreement.
The arguments remained inconclusive and are expected to continue on Tuesday before the bench of justices D K Jain and Madan B Lokur.
Earlier, a meeting between Tamil Nadu Chief Minister J Jayalalithaa and her Karnataka counterpart Jagadish Shettar in Bangalore to discuss the long-standing Cauvery water dispute failed last Thursday.
Jayalalithaa said the Karnataka government had refused to give water to Tamil Nadu.
Speaking to reporters after the meeting, Jayalalithaa said: "Karnataka flatly refused to release any water to Tamil Nadu."
"We will go before the Supreme Court and tell them the outcome of the meeting," she said.
The meeting occurred in the wake of the Supreme Court´s direction last Monday that asked both the Chief Ministers to meet and attempt to solve the problem in the larger interest of the farmers of both states.