A five-judge Constitution Bench headed by Chief Justice J S Khehar dismissed the pleas on the ground of delay in filing the petition and also on merit.
"The instant petitions have been filed by the petitioners for review of the judgement dated December 2, 2015 rendered by this court in the writ petitions and criminal appeal. The Review Petition Nos.560-564 of 2016 is barred by 208 days, whereas Review Petition (Crl.) No.27 of 2017 is barred by 358 days. There is no satisfactory explanation for condonation of such huge delay.
"Thus, though the present petitions are liable to be dismissed on the ground of delay itself, yet we have carefully gone the petitions for review, the judgement impugned and the papers connected therewith. We are satisfied that there is no error apparent on the face of the record of the case, warranting reconsideration of the judgement impugned. The instant petitions are without any merit," the bench also comprising Justices P C Ghose, S A Bobde, A M Sapre and U U Lalit said.
The verdict, which was passed by the bench on Tuesday, was made available on the apex court website on Wednesday.
"The review petitions are, accordingly, dismissed on the ground of delay as well on merits," the bench said.
The apex court had also rejected the prayer of the Tamil Nadu government and convict A G Perarivalan alias Arivu for open court hearing of the pleas.
The Tamil Nadu government had on July 28 last year moved the apex court seeking review of its judgement in the Rajiv Gandhi assassination case.
The petition had sought review of the apex court's verdict given in December 2015, virtually overturning the state government's clemency decision.
A five-judge bench had in 2015 said that the state governments must secure "concurrence" of the Union government before freeing convicts in certain cases.
The state government's review petition had said that as per the Criminal Procedure Code, the central government had no primacy in matters relating to remission or commutation of sentence and that it was "erroneous" on the part of the apex court bench to hold that the Centre had a "special status" under the constitutional scheme.
"In the case of remitting the sentence of the convicts, it is the state government which is the executive authority more competent to decide the outcome of such release/remission of convicted persons because of its proximity to the facts and circumstances relating to the case pertaining to conviction of the convicts," it said.
The court, which had settled questions arising out of the Tamil Nadu government's decision to free Gandhi's assassins, had dealt elaborately with the situations where the Centre will prevail over states' decision to grant remission which included cases where their powers are co-extensive, where trial has been held under central laws or conducted by agencies like CBI, or when they pertain to death penalty.
The Constitution Bench had said states cannot exercise "suo motu" the power to grant remission without any specific plea from the convicts.
The apex court had on February 20, 2014 stayed the Tamil Nadu government's decision to release three convicts -- Murugan, Santhan and Arivu, whose death sentence had been commuted to life term by it two days before.
The Supreme Court had later also stayed the release of four other convicts -- Nalini, Robert Pious, Jayakumar and Ravichandran, saying there were procedural lapses on part of the state government.
Santhan, Murugan and Arivu are at present lodged in the Central Prison, Vellore. The other four are also undergoing life sentence for their role in Gandhi's assassination on May 21, 1991 in Sriperumbudur, Tamil Nadu.
The Centre had asserted that the killers of former Prime Minister did nor deserve any mercy as the assassination was the result of a conspiracy involving foreign nationals.
The Tamil Nadu government, on the other hand, had said that the states have power to grant remission under the law and trashed accusations that its decision to release the seven convicts was "political and arbitrary".