According to video footage of the event, Mr Gandhi told voters in Uttar Pradesh, where he is a candidate for the nationalist BJP, that he would chop off the hands of anyone who “raised a finger” against Hindus.
“If someone thinks Hindus are weak or leaderless, if anyone raises a finger towards Hindus, then I swear on Gita that I will cut that hand,” he told a rally in Pilibhit, where communal violence has flared between Hindus and Muslims. He also allegedly compared a Muslim politician to Osama Bin Laden.
His comments were seen as a warning to Muslims in the area and were condemned by the Congress Party, led by his aunt Sonia Gandhi, as “unethical and against the law.”
Abhishek Singhvi, a Congress spokesman, said: “It is condemnable. He is associated with this party which has this anti-minority ideology and culture.”
Mr Gandhi insisted later that the footage had been tampered with. “The voice is not mine,” he said. “I don’t know who could be behind this.”
But his own party distanced itself from him, with one BJP colleague saying that the comments did not “reflect the BJP’s traditional culture”.
India’s election commission instructed officials in Uttar Pradesh state, where Mr Gandhi is running, to file a criminal case against him for “promoting hatred”. If convicted, he could be disqualified from running for office and jailed for up to five years.
Varun Gandhi is regarded as a future leader of the BJP, raising the intriguing prospect of India’s two main parties being led by the same dynasty which has given the country three prime ministers since independence. Mr Gandhi’s cousin, Rahul, is being groomed for the Congress Party leadership and is expected by many to be the party’s next prime minister.
The Gandhi family split after the death of Varun’s father Sanjay when his widow Maneka fell out with Indira Gandhi over her intention to play a political role in the Congress. Instead she joined the Janata Dal party and later served as environment, social justice and culture minister in BJP-led governments.