In the letter, in which he has called himself a "concerned citizen of India and Tamizh Nadu", Kamal said people were dismayed by the delay in setting up Cauvery Water Management Board and wanted justice.
"The Supreme Court has already performed its constitutional role by delivering the judgement. It is now the turn of your government to perform its constitutional duty and implement the order," he said.
Kamal pointed out how in his earlier role as Gujarat Chief Minister, Modi had the experience of water sharing amongst four states through the Narmada Control Authority.
"All sections of people of Tamizh Nadu have started to believe that this delay is due to ensuing elections in Karnataka and your party's interest in it. Sir, it is your duty as the Prime Minister to prove this wrong by immediately acting as per the Supreme Court order," Kamal added.