"I was not at home when the letter came this afternoon. My family received it. After reading the letter, written in English, the family informed the police... Currently, it is with the police," he told PTI.
Bhagwan had incurred the wrath of right-wing activists after he allegedly disparaged the Bhagawad Gita while speaking at a programme in Mysuru in February this year.
A Bajrang Dal local activist was arrested in Dakshina Kannada district a day after Kalburgi's death on August 30 for allegedly posting remarks on Twitter threatening Bhagwan for his 'derogatory' remarks on the Bhagawad Gita.
Stating that he is "not deterred" by such threats, Bhagwan said "it shows utter ignorance on the part of those who wrote the letter. They wouldn't have even read a page of my writing. I write on the basis of my research. If they have objections about it, they can always oppose it in a civilised way."
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"This is not the first time I have received such threats; I'm not afraid," he added.
"Yes, a letter threatening Bhagwan was received at his residence, we are investigating it," IGP (Southern Range) B K Singh said.
The murder of Kalburgi had prompted the state police to increase the security provided to Bhagwan. They had also extended security to other noted litterateurs, including Jnanpeeth award winner Girish Karnad and S L Byrappa.
77-year-old vocal and outspoken rationalist Kalburgi fell to the bullets of two unidentified men at his residence at Dharwad in north Karnataka on August 30.
Karnataka government has decided to hand over the Kalburgi murder case to CBI. The state CID would probe it till the central agency takes over.