The discussions took place in the backdrop of the Centre's plans to take a decision on notifying the final award of the Cauvery Water Disputes Tribunal.
Karnataka and Tamil Nadu are at loggerheads over the issue. The hearing in the Supreme Court today saw the states failing to sort out their differences on water sharing.
A bench of Justices R M Lodha and J Chelameswar posted the case for hearing on February 4 after the two states gave contradictory views on the issue.
Water Resources Minister Harish Rawat was specially invited for the deliberations on the issue, the second this month in the Congress Core Group headed by Gandhi.
Rawat is learnt to have told the top brass that it is legally binding for the government to notify the award.
The Centre has already informed the apex court that since the draft notification is pending with the Law Ministry, it is likely to take a final decision on the issue by January-end.
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The Centre had informed the Cauvery water sharing states -- Karnataka, Tamil Nadu, Kerala and Puducherry -- that it would notify the award by December-end, but the self-imposed deadline was missed as the issue is yet to be scrutinised by the Law Ministry.
In what was then described as a balancing act, the tribunal gave 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.
For environmental protection, it had reserved 10 TMC of water.
The tribunal's award will come into effect within 90 days of its notification by the Centre. As per law, the award comes into being after being notified by the Centre through its publication in a gazette.
The meeting of the Core Group was also significant as the Lokpal Bill is coming up before the Union Cabinet on Thursday, while plans by Congress MPs from Telengana to submit their resignations on the separate statehood issue has brought fresh concerns before the party leadership.