The Jesuit cleric is the sixteenth person to be arrested in the case, in which people have been booked under various sections of the Indian Penal Code and the anti-terror law UAPA.
Opposition BJP has dubbed the NCP's demand for withdrawal of cases as a "blatant support to naxalism".
The FIR was lodged against Navlakha and others by the Pune Police in January 2018 after the Elgar Parishad held in 2017 that had allegedly triggered violence at Koregaon Bhima in Pune district the next day.
Chandrashekhar alleged that the Narendra Modi government's decision to give 10 per cent quota to the general category poor is an attack on the Constitution and is aimed at serving the BJP's interests.
The five activists, Varavara Rao, Arun Ferreira, Vernon Gonsalves, Sudha Bharadwaj and Gautam Navlakha, are under arrest at their respective homes since August 29.