The cause of her death has not been announced. She was hospitalised on January 11 after being infected with what a doctor told Reuters was COVID-19. She is survived by her four siblings.
Mangeshkar died on Sunday morning of "multi-organ failure after more than 28 days of hospitalisation post COVID-19", said Dr Pratit Samdani, who was treating her at Mumbai's Breach Candy Hospital, according to Reuters TV partner ANI.
Mangeshkar's voice has rung out of television sets, on crackly airwaves and from movie theatres for most of independent India's three-quarters of a century, making hers the defining voice of many generations, and earning her the title of "the Nightingale".
Two days of national mourning will be observed with the national flag will flying at half-mast, Reuters TV partner ANI reported, citing government sources.
"I am anguished beyond words," Prime Minister Narendra Modi wrote on Twitter on Sunday.
"The kind and caring Lata Didi has left us. She leaves a void in our nation that cannot be filled. The coming generations will remember her as a stalwart of Indian culture, whose melodious voice had an unparalleled ability to mesmerise people."
Born in 1929 in pre-independence India, Mangeshkar began singing in her teens, and in a career spanning 73 years sang more than an estimated 15,000 songs in 36 languages.
She enthralled music-mad Indians with her lilting voice and sheer range, singing everything from patriotic songs to romantic numbers, both in films and albums.
The world of Bollywood - where movies were unthinkable without at least six songs and where everything from romance to grief was narrated with the help of a ballad - was where Mangeshkar cut her teeth and later made her name.
Other Bollywood personalities and politicians offered condolences.
"Love, respect and prayers," tweeted Oscar- and Grammy-winning Indian musician A R Rahman. Mangeshkar sang a number of his award-winning songs.
Classically trained, Mangeshkar moulded her voice to the demands of singing for Bollywood movies, even voicing songs in her 60s for an actress who was in her 20s.
Her songs motivated millions of Indians during wars with China and Pakistan to pay homage to the defence forces. Some of her songs are used as prayers in temples, shrines and schools.
Known for soft-spokenness and wearing a saree, her hair in two schoolgirl-like braids, Mangeshkar received India's highest civilian honour, the Bharat Ratna, in 2001. She was awarded France's highest civilian honour, the Legion of Honour, in 2009.
"Music is incomplete without your voice," actor Amitabh Bachchan said of Mangeshkar in 2019, commemorating her 90th birthday. "It has done the work of saints."
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