A bench comprising Chief Justice J S Khehar and Justice D Y Chandrachud allowed the plea of Tamil Nadu and posted the matter for further hearing after two months.
Tamil Nadu, in its plea on May 4, had sought execution of the apex court judgement in the case, saying it has been held that it will have a right to maintain the dam while its security would be taken care of by the Kerala police.
Kerala, in its reply to the execution petition, had denied all allegations of Tamil Nadu and said that the plea was "liable to be dismissed".
Kerala claimed that the right of access was not being denied but only regulated in the area as the security of the dam has been entrusted with it by virtue of the apex court order.
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Earlier, the apex court had rapped the Tamil Nadu government for seeking deployment of CISF for ensuring safety and security of the Mullaperiyar Dam, saying there cannot be a "perennial 'amrit dhara' kind of litigation", forcing the state to withdraw it.
Kerala had later moved the apex court for clarification on its verdict and contended that the water storage should not be increased to 142 feet until all the 13 spillover gates of the dam were operational.
The apex court had earlier too dismissed Kerala's plea to review its 2014 verdict, saying there was no reason to interfere with the judgement of the Constitution Bench.
The dam is situated in Idukki district of Kerala and is owned and operated by the Tamil Nadu government. The length of the main dam is 1200 feet and top of the dam is 155 feet.