The 79-year-old, whose party is in a controversial coalition with Prime Minister Narendra Modi's Hindu nationalist party in the Himalayan region, is likely to be succeeded as chief minister by his daughter.
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Sayeed died in hospital in New Delhi after being admitted on December 24 suffering from a respiratory illness, a hospital official told AFP.
His daughter Mehbooba Mufti, current head of the moderate People's Democratic Party (PDP) that he founded in 1999, is widely expected to take over as the state's first female chief minister.
He will be given a state funeral in Kashmir, with Modi expected to attend.
"Mufti Sahab's demise leaves a huge void in the nation and in J&K, where his exemplary leadership had a major impact on people's lives," the prime minister tweeted, using an honorific denoting respect.
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Sayeed's PDP controversially went into coalition in Jammu and Kashmir state with Modi's Hindu nationalist Bharatiya Janata Party after state elections at the end of 2014.
The PDP's main support base is among Muslims in the Kashmir Valley, the epicentre of the separatist insurgency that broke out in 1989, although the party stops short of calling for independence for the restive Himalayan region.
Analysts said the death of the veteran leader, who also served as chief minister in Kashmir between 2002 and 2005, was unlikely to trigger major change.
"The BJP and PDP have limited options and will try to continue in power," said Happymon Jacob, assistant professor of international studies at New Delhi's Jawaharlal Nehru University.
"But Mehbooba is a bit immature when it comes to the administrative part. She has never held any position in the government and has to start from scratch in an alliance with an ideologically disparate partner."
Sayeed, a former lawyer, was appointed India's first Muslim home minister in 1989.
Later the same year another of his daughters was kidnapped by Kashmiri militants. She was eventually released in exchange for five jailed rebels.
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His party won the 2002 election in Kashmir on a promise to bring a "healing touch" to the war-ravaged region, and Sayeed has won praise for his efforts to bring about reconciliation.
But he also faced criticism at home for his perceived closeness to New Delhi. A profile of the chief minister in the latest issue of Indian magazine The Caravan was headlined "The Collaborator -- How Mufti Mohammad Sayeed became Delhi's man in Kashmir".
Several rebel groups have for decades been fighting Indian forces deployed on the Indian side of divided Kashmir, seeking independence or a merger of the territory with Pakistan.
The fighting has left tens of thousands dead, mostly civilians.
The region is divided between India and Pakistan, both of which claim the Himalayan territory in its entirety.
Sayeed's body will be flown on Thursday to Kashmir, where his funeral is expected to take place later in the day.
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