A division bench of the Islamabad high court had dismissed the petitions filed by the Federal Investigation Agency on September 14 as prosecutors had not pursued them for months.
The same bench on Thursday restored the two petitions following a request from the FIA.
One petition asked the court to direct authorities to obtain the voice samples of the seven Pakistani suspects, including Lashkar-e-Tayiba commander Zakiur Rehman Lakhvi, so that they could be compared with samples provided by India of communications between the attackers and their Pakistan-based handlers.
The other petition asks the court to declare Kasab a fugitive in order to complete certain legal requirements that will help speed up the trial of the seven suspects by a Rawalpindi-based anti-terrorism court.
Investigators have said such a move will also help them complete their probe against the seven suspects.
The petitions were filed by the FIA in February.
As no one from the FIA appeared in court to pursue the petitions, the high court had dismissed them last month.
During a hearing held on Thursday, FIA special public prosecutor Chaudhry Zulfiqar Ali told the high court that prosecutors could not appear before it during several hearings for "certain reasons". He did not give details.
Ali urged the bench to restore the petitions as they were directly linked to the trial of the seven suspects by the anti-terrorism court.
He pointed out that the anti-terrorism court had also issued non-bailable warrants for Kasab and his alleged accomplice Fahim Ansari.
Kasab is on death row in an Indian prison while Ansari continues to be in custody though a court in Mumbai has acquitted him in the Mumbai attacks case.
In May 2010, the FIA had submitted an application in the anti-terrorism court that asked for the trial of Kasab to be separated from the trial of the seven Pakistani suspects.
However, the anti-terrorism court rejected the application.
In the two petitions that were revived yesterday, the FIA has contended that the anti-terrorism court's order was erroneous.
The FIA has requested the high court to direct the trial court to declare Kasab as a proclaimed offender.
The FIA has also contended that it is essential to obtain the voice samples of the seven Pakistani suspects so that they can be compared to samples provided by Indian authorities.These samples are a "very important piece of evidence" and could help prosecutors establish the guilt of the accused.