He was 84.
Konar, a leading figure in the militant peasants' movement in the state during 1960s and early 1970s, is survived by his wife, two sons and two daughters.
A former CPI-M central committee and state secretariat member, Konar was the party's prominent peasant leader from Burdwan district.
A former party legislator, he was elected to the West Bengal Legislative Assembly from Memari constituency in Burdwan district three times - in 1969, 1971 and 1977.
Konar was elected as chairman of the five-member CPI-M central control commission in 2012, an internal vigilance wing of the party.
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Konar had not been keeping well for the last several months.
He was known for making caustic remarks against the Trinamool Congress and its chief Mamata Banerjee which had drawn flak even from allies during Singur and Nandigram agitations.
Konar had also taken potshots against the then West Bengal Governor, Gopalkrishna Gandhi, after the Nadigram killing in 2007.
Taking exception to Gandhi's description of the Nandigram outrage as a "cold horror", Konar had said at a public meeting "Gandhi should come out of Raj Bhavan and carry the Trinamool flag."
Konar served as the national president of the CPI-M's peasants' front All-India Kisan Sabha for years and was the organisation's vice-president at the time of his death.
He was also the secretary of the state CPI(M)'s peasant wing Paschimbanga Pradeshik Krishak Sabha.