Indu Makkal Katchi, a Hindu outfit, claimed to have sent the letter along with the cheque to Madras High Court judge Justice C S Karnan, asking him to migrate to any country, if he so desired.
IMK President Arjun Sampath, in the letter, criticised the judge for speaking against the judicial system in India, "thus disrespecting the Constitution."
Sampath referred to Justic Karnan's recent remarks that he was a victim of caste discrimination in the judicial system and that if his birthright was cancelled, he would migrate to another country where there was no caste discrimination.
"If Karnan accepts the cheque, he has to mention which county he is migrating to," he said to a question.
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Sampath said he has also written to Prime Minister Narendra Modi on the issue and requested him to take stringent action against Karnan and allow him to migrate to any country of his choice.
Justice Karnan had on February 15 "stayed" the Chief Justice of India's order, transferring him to Calcutta High Court, which was suspended later that day by the Supreme Court with a direction that he not be assigned any judicial work.