The court was hearing a plea on the matter by AG Perarivalan, one of the convicts whose death sentence was commuted to life term in the assassination case.
He has alleged that neither the CBI's special investigation team, nor the Multi Disciplinary Monitoring Agency (MDMA) headed by it, had proceeded with the probe in a proper perspective to bring the accused to book, as several top people were involved in it.
"This has to be investigated. May be not at his (petitioner's) instance, but this needs investigation," a bench, comprising Justices Ranjan Gogoi and Navin Sinha, said.
The bench asked the CBI to file a detailed investigation report along with a time-frame within which the probe would be completed. It also directed the agency to indicate the legal hurdles, if any, and the steps taken to overcome these issues.
During the hearing, Additional Solicitor General Maninder Singh told the top court that investigation was going on and it would take some time as some accused were absconding.
He said the matter would require extradition proceedings since some of the absconding accused were out of India.
To this, the bench asked "is it the stand of the government that as on today, investigation into these aspects can go on?"
Responding to the query, Mr Singh said "yes" but it would take some time.
He argued that the CBI has already filed a counter affidavit in the matter and that Mr Perarivalan's conviction has been upheld by the top court, while the probe into several aspects of the case was going on.
"With or without him (Perarivalan), this matter has to be investigated. What benefits he may get out of the investigation will be seen later," the bench said and fixed the matter for hearing on August 16.
The top court had earlier sought the response of the centre and the CBI on the plea which has alleged that CBI did not probe the conspiracy behind the killing of Rajiv Gandhi in 1991 despite an order from a TADA court in Chennai.
The top court had on Febraury 18, 2014 commuted the death sentence of Mr Perarivalan to life imprisonment, along with two other condemned prisoners -- Santhan and Murugan - on grounds of a delay of 11 years in deciding their mercy plea by the Centre.
Mr Perarivalan had earlier sought the case dairies pertaining to CBI and MDMA, which had probed the matter.
He had also referred to the inquiry report of the Justice Jain Commission that had probed the conspiracy aspect of the assassination and which had formed the basis for the TADA court's order for a further probe to identify the role of individuals to uncover the larger conspiracy in the murder.
The convict had alleged that the CBI and the MDMA, which were entrusted with the task to probe the facts, have not done their work properly.
"The grievance of the petitioner is that the designated TADA Court was monitoring the pending investigation on paper only, but without knowing the actual facts of the investigation being conducted by CBI (MDMA) for the last about 17 years.
"The TADA Court merely collected sealed covers cluelessly, that too in-chambers video in-camera proceedings, from the investigating agency every three months, once without even opening the said covers for so many years," the plea has claimed.
Rajiv Gandhi was assassinated on the night of May 21, 1991 at Sriperumbudur in Tamil Nadu by a suicide bomber at an election rally.