Top Congress leaders took part in the march that culminated in a demonstration. Leaders of other parties also joined the protest as a mark of solidarity.
CBI chief Alok Verma filed the writ petition under Article 32 of the Constitution of India, as per which individuals may seek redressal for any violation of their fundamental rights.
Congress on Wednesday launched a sharp attack on Prime Minister Narendra Modi alleging that CBI war is "a desperate cover-up attempt" over the Rafale deal.