The bench, also comprising Justices A M Khanwilkar and D Y Chandrachud, said the Cauvery Water Disputes Tribunal's award, which was modified by the top court, has to be taken to the logical conclusion by the Cauvery Management Scheme.
It also dismissed Tamil Nadu's plea seeking initiation of contempt against the centre for non-finalisation of the Cauvery scheme.
Karnataka, which is facing political tug of war between BJP and Congress-JDS over government formation, had earlier made a failed bid to temporarily stall the finalisation of draft Cauvery management scheme.
The top court had made it clear that it would see that the draft scheme is "in consonance with its judgement only."
Earlier, the bench had red-flagged the provision empowering the centre to issue the directions, saying "this part (power of centre to issue directions) of the scheme is not in consonance with the judgement. We make it clear to you".
The top court, in its verdict delivered on February 16, had asked the centre to frame the Cauvery management scheme, including creation of the Cauvery Management Board, for release of water from Karnataka to Tamil Nadu, Kerala and Puducherry.
The scheme, once finalised, would deal with the issue of water share of the four states in different circumstances like normal and deficient water years in the Cauvery River basin.
The top court had modified the Cauvery Water Disputes Tribunal (CWDT) award of 2007 and made it clear that it will not be extending time for this on any ground.
It had raised the 270 thousand million cubic feet or tmcft share of Cauvery water for Karnataka by 14.75 tmcft and reduced Tamil Nadu's share, while compensating it by allowing extraction of 10 tmcft groundwater from the river basin, saying the issue of drinking water has to be placed on a "higher pedestal".