"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," Mr Bhagwan told PTI on Wednesday, Sept 9.
Mr Bhagwan had angered right-wing activists after he allegedly disparaged the Bhagavad Gita while speaking at a programme in Mysuru in Feb 2015.
A local activist from the Bajrang Dal was arrested in Dakshina Kannada district a day after Mr Kalburgi's death on Aug 30 for allegedly posting remarks on Twitter, threatening Mr Bhagwan for his 'derogatory' remarks on the Bhagavad Gita.
Mr Bhagwan's family spoke to him about the contents of the letter which said that "three people we have finished, next is your turn; no amount of police protection will help. Your time is over, count the days."
Stating that he is "not deterred" by such threats, Mr 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."
"This is not the first time I have received such threats; I'm not afraid," he added.
Police are now examining the letter and its origin.
"Yes, a letter threatening Bhagwan was received at his residence, we are investigating it," IGP (Southern Range) BK Singh said.
The murder of Mr Kalburgi had prompted the state police to increase the security provided to Mr Bhagwan. They had also extended security to other noted litterateurs, including Jnanpeeth award winner Girish Karnad and SL Byrappa.
Mr Kalburgi, 77, was shot dead by two unidentified men at his residence at Dharwad in north Karnataka on August 30.
The state government has decided to hand over the murder case to the Central Bureau of Investigation or CBI. The Criminal Investigation Department (CID) of the state police will probe it till the central agency takes over.