Parkar, who is over 80, was brought to the court on a stretcher from a hospital in Byculla, while 75-year-old Zebunisa, suffering from cancer, came on a wheel-chair.
They were slated to surrender on May 17, but failed to give themselves up because of ill-health.
While Parkar had been admitted to hospital last Thursday for chest pain, Zebunisa had been advised to undergo certain medical tests.
Today, when Judge G A Sanap saw Parkar on the stretcher, he suggested that he may be taken outside awhile to breathe some fresh air.
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Fellow convict, actor Sanjay Dutt, for whom May 16 deadline had been set by Supreme Court, has already surrendered.
Earlier, Parkar and Kazi had sought more time to surrender citing medical grounds, but the TADA court rejected their applications, saying that it could not tinker with the Supreme Court-set deadline.
On May 17, TADA court also issued non-bailable warrants, but they were not executed.
Parkar was convicted by the TADA court for his role in organising the landing of arms and RDX in Raigad district prior to the March 1993 serial blasts, and in arranging a conspiracy meeting.