The decision by Rawalpindi bench of the Lahore high court, comprising of justices Rauf Ahmed Sheikh and Hasan Raza Pasha was made after hearing the arguments by the advocate for the Federal Investigation Agency (FIA).
The Federal Investigation Agency had filed the petition on Apr 10.
The High Court's decision on the admissibility of the petition is yet to be determined.
Earlier, Special Investigation Group of the FIA, probing the Pakistani links to the 2008 Mumbai attacks, had appealed against an anti-terrorism court's decision to reject the appeal to declare Kasab and Ansari as 'proclaimed offenders' or fugitives.
According to sources FIA believed that the appeal would pave way for using the confessional statements of Kasab and Ansari in the ongoing 26/11 trial in Pakistan against the seven accused- Lashker-e-Toiba (Let) commander Zakiur Rehman Lakhvi, Zarar Shah, Hamad Amin Sadiq, Abu al-Qama, Shahid Jamil Riaz, Younas Anjum and Jamil Ahmed.
However, the anti-terrorism court rejected FIA's request in the order issued on Mar 27, on the ground that Ajmal and Ansari were in the custody of Indian authorities and were facing trial in a court in Mumbai in connection with the 2008 Mumbai terror attacks.