Ms Jayalalithaa, who had been admitted to hospital in September for respiratory troubles, suffered a cardiac arrest on Sunday evening -- hours after her party said the doctors have pronounced her fully recovered.
Amma to legions of her supporters, Jayalalithaa's death triggered an outpouring of grief from millions of supporters.
Messages of condolence, meanwhile, poured in from across the political spectrum.
In a series of tweets, Prime Minister Narendra Modi expressed his grief and solidarity with the people of Tamil Nadu.
I will always cherish the innumerable occasions when I had the opportunity to interact with Jayalalithaa ji. May her soul rest in peace.
- Narendra Modi (@narendramodi) December 5, 2016
President Pranab Mukherjee sent in messages of condolence.My thoughts and prayers are with the people of Tamil Nadu in this hour of grief.
- Narendra Modi (@narendramodi) December 5, 2016
In her passing away, the nation has lost an icon who was loved and admired by millions #PresidentMukherjee
- President of India (@RashtrapatiBhvn) December 5, 2016
Ms Jayalalithaa's arch-rival, DMK chief M Karunanidhi, offered his heartfelt condolences. "I offer deep condolences on the passing away of Jayalalithaa... the wishes of lakhs of her followers will make her immortal," he said. His son Stalin called it "an irreparable loss to Tamil people".
In her tribute, Congress President Sonia Gandhi hailed her as a "towering figure in our national and political life, who won admiration across the political spectrum for the intrepid spirit with which she faced the ups and downs of her life in politics."
"As the leader of AIADMK and four-time Chief Minister of Tamil Nadu, she had a unique and deep empathy with the needs and hopes of the people, and put in place policies that immeasurably improved their lives," she said.
Senior Union ministers and other political leaders expressed grief. Messages poured in from leaders from across the political divide.
Saddened by the demise of Tamil Nadu CM J.Jayalalithaa ji. I extend my deepest condolences to her party and followers in this hour of grief.
- Amit Shah (@AmitShah) December 5, 2016
V sad to hear the demise of Amma. A very very popular leader. Aam admi's leader. May her soul rest in peace.
- Arvind Kejriwal (@ArvindKejriwal) December 5, 2016
Recalling the "affection she showed me each time we met," Union minister Nirmala Sitharaman tweeted, "Her life's journey is a story of grit & perseverance... Understood the mind of the poor & the women. Stayed connected to her people".
Popular,strong,bold,efficient, people- friendly,charismatic leader,
- Mamata Banerjee (@MamataOfficial) December 5, 2016
Amma.Always at the heart of people. Big loss.I am shocked,saddened 1/2
Deeply saddened to hear demise of #Amma , a Pro poor, Popular,Bold, Strong & result oriented Leader of country.Truly u wil be dearly missed
— Lalu Prasad Yadav (@laluprasadrjd) December 5, 2016
"In deep anguish over the demise of Tamil Nadu CM Jayalalithaa, a long-time friend & a leader with indomitable spirit who is loved by all," tweeted Andhra Pradesh Chief Minister Chandrababu Naidu.
Assam Chief Minister Sarbananda Sonowal called her one of India's "tallest leaders".
Tamil Nadu Chief Minister #Jayalalithaa's passing away is a great loss to the state & it's people, we stand by them in this hour of grief.
— ShivrajSingh Chouhan (@ChouhanShivraj) December 5, 2016
Earlier in the evening, erroneous reports of her death in local television channels had triggered violence outside Chennai's Apollo hospital, where Jayalalithaa had been admitted for more than three months.
Wailing and grieving, supporters broke down barricades in an attempt to enter the hospital. Others threw stones at the policemen who had deployed outside the hospital to control the crowds.
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