Prosecution lawyers informed Judge Rana Nisar Ahmed of the Rawalpindi-based anti-terrorism court that they needed more time to withdraw the petition as it was yet to be listed by the Lahore High Court.
The judge accepted the request and adjourned the case till January 22.
Seven suspects, including Lashker-e-Taiba commander Zakiur Rehman Lakhvi, have been charged with planning, facilitating and financing the 2008 Mumbai terror attacks.
Legal experts have contended that the issue of the petition in the Lahore High Court must be settled before proceedings in the anti-terrorism court can move forward.
The lawyers of the Federal Investigation Agency had approached the Lahore High Court last year after the anti-terrorism court rejected a petition for Kasab and Ansari to be declared proclaimed offenders or fugitives.
Pakistani national Kasab, the lone surviving attacker, was sentenced to death by a court in Mumbai for his role in the attacks on India`s financial hub that killed 166 people in November 2008.
Ansari, an Indian national, was acquitted by the same court but he continues to be in custody in connection with other cases.
In another development, defence lawyer Shahbaz Rajput on Saturday submitted testimonials on the authenticity of his law degree in response to allegations by prosecutors that he possessed a fake degree and should be barred from appearing in court.
At the last hearing, the prosecution team produced a FIR filed against Rajput by officials of the Rawalpindi Bar Association that alleged he possessed a fake law degree.
Rajput told PTI that he had submitted documents and testimonials on the authenticity of his degree.
He had earlier described the prosecution`s move as a bid to "pressurise" him to stop acting as counsel for the suspects accused of involvement in the Mumbai attacks.