Shettar said there should be no process of issuing a final notification as Karnataka had remonstrated about the tribunal award and filed a petition before the Supreme Court.
"An all-party delegation will meet Prime Minister soon...." he said in the Assembly, which is holding its session here.
The Tribunal has awarded Tamil Nadu 419 TMC of water(as against the demand of 562 TMC); Karnataka 270 TMC (as against its demand of 465 TMC); Kerala 30 TMC and Puducherry 7 TMC.
At a meeting of the Cauvery Monitoring Committee in Delhi on December 7, states sharing the Cauvery waters were informed that the final CWDT award would be notified by the end of this month.
Shettar said he had written to Singh urging him to call a meeting of Chief Ministers of the riparian states to discuss the pros and cons of the final notification of the award.
Water Resources Minister Basavaraj Bommai said the apex court has not given any fresh direction to the state on release of Cauvery water to Tamil Nadu. "Abiding by the apex court direction, the state had to release 10,000 cusecs of water for a week," he added.
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Bommai said the Centre took a "unilateral decision under influence" and without consulting the Attorney General or seeking the opinion of the Union Law Department.
"The CMC cannot take any decision on issuing the final notification. It acted beyond its jurisdiction," Bommai said.
Karnataka had stopped releasing water to Tamil Nadu since Sunday evening after it had started releasing 10,000 cusecs since the night of December 6. A day later, CMC asked the state to provide Tamil Nadu with 12 TMC of water during December.
The Supreme Court had yesterday made it clear that it will not interfere with the CMC's order directing Karnataka to provide Tamil Nadu with 12 TMC of water during December despite both warring states being dissatisfied with the award.