Mufti Mohammed Sayeed, who took over as the top elected official of the region in March last year, was hospitalized two weeks ago in the Indian capital.
His death was announced by party leader and Kashmir state Education Minister Nayeem Akhter.
Sayeed is survived by his wife, three daughters and a son. Mehbooba Mufti, one of his daughters, is expected to succeed him as the chief minister of the Indian portion of Kashmir.
His body will be taken to Srinagar, the main city in Kashmir, and buried in his ancestral village, said Akhter.
Prime Minister Narendra Modi said that Sayeed "provided a healing touch to Kashmir through his leadership."
India and Pakistan have fought two wars over control of Kashmir, divided between them since 1947.
Mufti advocated a dialogue with Pakistan to settle the dispute, and sought to promote trade and travel between the divided parts of the Himalayan region.
At the start of insurgency in the Indian portion of Kashmir in 1989, rebels abducted one of Sayeed's daughters. He was India's home minister then.
His daughter was later freed in exchange for the Indian government releasing five militants from prison.
Sayeed became the chief minister of the Indian portion of Kashmir, with the Hindu nationalist Bharatiya Janata Party as a junior partner in the government after no single party won a clear majority in state elections.
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