A five-judge constitution bench of the court headed by Justice DK Jain, while permitting the two warring states to get copies of the report in a sealed cover, posted the matter for further hearing to July 23.
Senior counsel Harish Salve and Rajiv Dhawan, both appearing for Kerala, today told the bench that the state was willing to evolve a "political consensus" on the vexed dam issued.
"Both states should sit together and evolve a political consensus on the issue," the counsel told the bench which responded by saying, "We can only wish and hope".
The Empowered Committee, set up by the apex court in February 2010 to look into all aspects of the dam, had submitted its report to the apex court in a sealed cover on April 25.
The five-member committee headed by former Chief Justice of India AS Anand, which had finalised the report, is understood to have focused on all aspects of the 119-year-old dam including its safety. There has been tension between the two states over the safety of the dam.
While Tamil Nadu contends that the dam is safe and its water level has to be raised from 132 ft to 136 ft, Kerala says the structure is weak and it has to be replaced with a new dam.
As tensions rose between the two states in December last year, a two-member technical team of the Empowered Committee visited the site and is understood to have concluded that recent tremors in that region did not have any impact on the Mullaperiyar Dam and that it was safe. The committee's tenure was extended in February to enable it to complete its report.