As part of the stringent conditions imposed on his interim bail by the HC, Rao has been staying with his wife at a rented accommodation in Mumbai.
The agency urged the court to not stay the trial proceedings in the interim before the special court.
Rao (82), who was granted interim bail on medical grounds in February 22 this year, was scheduled to surrender and return to judicial custody on September 5.
Elgar Parishad case: No NIA action till HC hears Varavara Rao's medical bail extension plea on September 6
Rao's counsel, senior advocate Anand Grover, sought an extension of bail before a bench of Justices SS Shinde and NJ Jamadar on Friday.
NIA gets 2 weeks to reply on pleas of Bharadwaj, Navlakha seeking clone copies of all seized devices
Bharadwaj and Navlakha had approached the high court last month seeking such copies.
Will get activist Navlakha medically examined, says Maharashtra government; HC seeks NIA's reply on his plea for house arrest
In his plea, Navlakha, 69, also sought that he be placed under house arrest as part of his judicial custody, owing to his advanced age and a host medical ailments that he suffers from.
The arrested accused in the case include activists Sudha Bharadwaj, Vernon Gonsalves, Varavara Rao, Hany Babu, Anand Teltumbde, Shoma Sen, Gautam Navlakha and others.
Babu was sent to the private hospital in May this year following an order of the Bombay High Court.
The special court will consider the draft charges on August 23 and then frame charges against the accused, who included several activists.
Singh made the submissions before a bench of Justices SS Shinde and NJ Jamadar, which is hearing a plea filed by Bharadwaj seeking default bail.
The court further said there is no hitch to record prima facie satisfaction that there is material against the applicant to show his complicity in the crime.
Bharadwaj, in jail since September 2018, has sought bail on the technical ground that the court which took cognizance of the charge sheet initially lacked the power to do so.
Elgar Parishad case transferred to NIA as it pertains to national security: Probe agency to Bombay HC
The affidavit said the primary objective to establish the NIA was to better tackle cross-border crimes with inter-state and international originations and ramifications.
Raut said Stan Swamy died in custody while Prime Minister Narendra Modi held talks with those who want autonomy for Kashmir and are demanding restoration of Article 370 there.
At every turn, the Government had made it clear that it was out to get Stan Swamy. This is the central fact that needs to be understood and recorded.