Keishing, a Naga, served as the chief minister of Manipur from 1980 to 1988 and from 1994 to 1997.
Keishing passed away around 8.15 pm due to multiple organ failure, doctors attending him at the Regional Institute of Medical Sciences (RIMS) said.
He was hospitalised on July 1 after his health condition worsened. He is survived by two sons and four daughters.
In Delhi, Home Minister Rajnath Singh condoled the demise of Keishing, and described him as a "towering leader" from Manipur who believed in humanity, social harmony and clean politics.
"I am pained by his demise, I offer my heartfelt condolences to the bereaved family of Shri Keishing. My thoughts are with his family in this hour of grief", he tweeted.
Union minister of state for home Kiren Rijiju also expressed grief. In a Twitter post, Rijiju remarked that despite being 96-year-old, Keishing "remained so fit till date".
The Manipur government has declared that all government offices and educational institutions will be closed tomorrow as mark of respect to Keishing.
Manipur Governor Najma Heptulla expressed her sadness and condoled the demise of Keishing.
Congress President Sonia Gandhi also expressed condolence, saying she is deeply saddened by the demise of one of the senior most leaders with a sterling record of public service of nearly 70 years.
"In his death, we have lost an important connect with our glorious past that will be hard to recoup", she said.
Party vice president Rahul Gandhi also mourned Keishing's demise.
"Ex CM & Parliamentarian Rishang Keishing was a true Congressman & one of the tallest leaders of North East. Very sad to know of his passing (sic)", said a post on Rahul's official Twitter handle.
West Bengal Chief Minister Mamata Banerjee also condoled the demise of Keishing.
"Saddened at the passing of Rishang Keishing a long-serving CM of Manipur in the 1980s, former RS MP. Condolences to his family and wellwishers", she said in a tweet.