A bench of Justices Ranjan Gogoi, Navin Sinha and KM Joseph listed the matter for further hearing after four weeks.
Advocate G Sivabalmurugan, appearing for petitioner S Abbas and three others, said their writ has been pending since 2014 when they had challenged the first decision of then J Jayalalithaa-led government to release the seven convicts.
He sought permission to file additional documents and amend the petition, saying recently, the Tamil Nadu government has again decided to release these convicts.
After Sivabalmurugan said several orders have been passed by the apex court since 2014 with regard to the case and he needed to put it on record, the bench asked him to file the additional documents.
S Abbas, now 35, was eight years old when his mother had died in the blast triggered by an LTTE suicide bomber in which the former Prime Minister was killed at Sriperumbudur in Tamil Nadu on May 21, 1991.
On September 6, in a separate case, the apex court had asked the Tamil Nadu Governor to consider the mercy petition of AG Perarivalan, a convict in the 1991 Rajiv Gandhi assassination case.
The Centre had on August 10 told the apex court that it does not concur with the Tamil Nadu government's proposal of 2014 to release the seven convicts in the Rajiv Gandhi assassination case, claiming remission of their sentence will set a "dangerous precedent" and have "international ramifications".
On August 20, 47-year old Perarivalan alias Arivu had told the apex court that no decision has been taken as yet on his mercy petition filed before the Tamil Nadu Governor over two years ago under Article 161 of the Constitution. He had filed the petition on December 30, 2015, saying he had suffered over 24 years of solitary/single confinement.
He was charged with supplying a 9-volt battery which was allegedly used for the belt bomb that had killed Gandhi and 14 others.
Convicts Perarivalan, V Sriharan alias Murugan, T Suthendraraja alias Santham, Jayakumar, Robert Payas, P Ravichandaran and Nalini have been in jail for more than 25 years.
Rajiv Gandhi was assassinated on the night of May 21, 1991 at Sriperumbudur in Tamil Nadu by a woman suicide bomber, identified as Dhanu, at an election rally. Fourteen others, including Dhanu herself, were also killed.
This was perhaps the first case of suicide bombing which had claimed the life of a high-profile global leader.
The apex court had on February 18, 2014, commuted the death sentence of three convicts - Murugan, Santhan and Perarivalan - citing inordinate delay by the executive in deciding their mercy plea.
After Gandhi's assassination, the probe was transferred from the state police to a Special Investigation Team of the CBI at the request of the Tamil Nadu government.
The SIT had named 41 accused in its charge sheet - including 12, who died in the blast and three who were absconding - before a TADA court in Chennai. The prolonged trial culminated in 1998, when the TADA court sentenced 26 of the accused to death.
In May 1999, the apex court had upheld the death sentence of four, including Murugan, Santham, Perarivalan and Nalini, commuted the death sentence of three to life, and freed the remaining 19.
In April 2000, the Tamil Nadu Governor had commuted the death sentence of Nalini on the basis of state government's recommendation and an appeal by Rajiv's wife and then Congress President Sonia Gandhi.
The death sentence of the remaining three convicts were commuted in February 2014 by the apex court on grounds of inordinate delay of 11 years in deciding their mercy petitions.