The matter came up for hearing before a three-judge bench of Justices N.V. Ramana, B.R. Gavai and R. Subhash Reddy.
Justice Gavai recused to hear the matter. Therefore Justice Ramana said the matter will be heard by another bench on October 3.
Earlier, Chief Justice Ranjan Gogoi had recused to hear Navlakha's plea.
The Bombay High Court on September 13 rejected Navlakha's plea seeking to quash the FIR filed against him early last year by the Pune Police for his alleged Maoist links and involvement in the Bhima-Koregaon and Elgar Parishad cases.
Soon after the Bombay High Court rejected his plea, the Maharashtra government filed a caveat in the Supreme Court anticipating Gautam Navlakha's appeal against the High Court's order.
A caveat means that the court cannot pass an order without hearing the other side.
Navlakha and nine other human rights and civil liberties activists were arrested in the case by Pune Police from different parts of India, for their role in the December 31, 2017 Elgar Parishad held in Pune, which served as a trigger for the caste riots in Bhima-Koregaon the next day on January 1, 2018.
Among other things, they were charged with alleged links with the banned CPI-Maoist, a conspiracy to assassinate Prime Minister Narendra Modi and to overthrow the elected government.
( With inputs from IANS )