The dam is located on the Western Ghats near Thekkady in Idukki district of Kerala on the Periyar river.
The apex court fixed the matter for hearing on July 11.
A five-judge constitution bench headed by Chief Justice Dipak Misra reserved its verdict on a plea seeking recognition of 'living will' made by a terminally-ill patient for passive euthanasia.
The Supreme Court on Wednesday suspended all court proceedings in India relating to the trial of two Italian marines in connection with the 2012 killing of two fishermen off Kerala coast.
The apex court imposed four conditions on the marine.