Deshpande, a Rajya Sabha member, was not keeping well for the past two-three days, and she died in her sleep early Thursday morning, Rajshree, one of her close associates said.
"Deshpande had returned from Dhanbad on Tuesday and had some gastric problems. She was suffering from fever from last evening," she said.
A noted Gandhian and a Rajya Sabha member, Nirmala Deshpande, is best known for her efforts to promote Gandhian ideology, eschew communal violence and usher in peace between India and Pakistan.
Popularly known as 'Didi' to her followers, 79-year-old Deshpande, clad in white khadi saree, was a familiar figure at functions at institutions connected to the Father of the Nation.
Having taken a vow not to get married, Deshpande dedicated her entire life to the promotion of the work and principles of Gandhi and served the deprived and the downtrodden.
Her tryst with destiny began in 1952 when she joined the Bhoodan Movement and stayed at Acharya Vinoba Bhave's Paunar Ashram at Wardha near Nagpur. She undertook 40,000 kilometers of padyatras along with Bhave to carry the message of Gram Swarajya from state to state.
During the historic march, they collected thousands of acres of land donated by those who believed in Gandhiji's ideals and distributed it among poor and landless people.
In eighties and nineties, she was the moving spirit behind various peace marches in Punjab and Kashmir. Her peace mission to Kashmir in 1994 and her initiative to organise Indo-Pak meet in 1996 were among major achievements in her decades of public service career.
She was conferred the prestigious Rajiv Gandhi National Sadbhavana Award for promoting peace and communal harmony.
Prime Minister Manmohan Singh on condoled the demise of Nirmala Deshpande, describing her as a "living Gandhian".
She was deeply committed to "creating a good society based on Gandhian values of simplicity, decency and honesty", he said in a condolence message.
Congress President Sonia Gandhi also condoled the death of veteran Gandhian Nirmala Deshpande, saying she was a person of rare courage and compassion, deeply imbued with Gandhian values.
Pak social worker laments death
Eminent Pakistani social worker Abdul Sattar Edhi condoled the death of Indian parliamentarian and veteran Gandhian Nirmala Deshpande, sayingshe had played a key role in promoting Indo-Pak ties.
In a message, Edhi and his wife Bilquis Edhi expressed grief and sorrow at the death of 80-year-old Deshpande, who died in her sleep early on Thursday morning in New Delhi.
Noting that Deshpande was a pioneer in the independence movement along with Mahatma Gandhi, the couple said she had "played a vital role in promoting India-Pakistan friendship".
Bilquis Edhi said Deshpande had been impressed by her husband's social work and had been translating his biography into Hindi.
Her death had created a void in India and Pakistan and she would miss a "humanity loving friend", Bilquis said in her message.
Along with many other dignitaries, senior Pakistani politician Sherry Rehman will also attend the funeral.