Gandhi, 29, is a member of the Bharatiya Janata Party in spite of being descended from two Congress Party prime ministers, Nehru and Indira Gandhi, Nehru's daughter. The BJP was originally a Hindu nationalist party but has been distancing itself from Gandhi since his alleged remarks were made public.
He is now a candidate for the parliamentary seat formerly held by his mother, Maneka Gandhi, in Uttar Pradesh, the Indo-Asian News Service said.
Gandhi asked why, if he had made the alleged remarks at an election rally on March 4, the video was not released for more than a week.
"I am a Gandhi, a Hindu and an Indian in equal measure and my attempt was not to spread ill-feeling against any community and I stand by all religion and all faiths," Gandhi said. "I am a victim of a political conspiracy ... Those are not my words, that is not my voice. I want to ask the nation to stand by me."
Gandhi said that Hindus in Uttar Pradesh are under attack.
Kate Moss Playboy shoot is classic Playboy, classic Kate
Man behind Doritos Locos Tacos passed away on Thanksgiving