The 98-year-old monk had been undergoing treatment for age-related ailments since February, 2015.
A statement released by the Ramakrishna Math and Ramakrishna Mission, Belur Math, said, "Despite the best medical attention, his condition deteriorated over the last few days and he passed away around 5.30 PM today at Ramakrishna Mission Seva Pratishthan hospital."
The cremation will take place at Belur Math tomorrow at about 9.30 pm and the gates of Belur Math would remain open tonight and tomorrow till the last rites were completed, it stated.
As a young boy, Modi had visited the Belur Math to join the Order, but his request was turned down and he was told that his calling was elsewhere.
Later, he got spiritual guidance from Swami Atmasthananda in Rajkot, Gujarat.
West Bengal Chief Minister Mamata Banerjee also condoled the demise of the monk.
Atmasthanandaji, born in May, 1919, at Sabajpur, near Dhaka, now in Bangladesh, had received "mantra diksha" from Swami Vijnananandaji Maharaj (a monastic disciple of Ramakrishna) in 1938 and joined the Ramakrishna Order at Belur Math in January, 1941 at the age of 22.
After serving the Order at Belur Math and the branches at Deoghar (Vidyapith) and Mayavati (Advaita Ashrama), Atmasthanandaji got the opportunity to serve Swami Virajanandaji Maharaj, the then president of the Order, for a long time.
He spent several years in the company of Virajanandaji Maharaj at the Shyamla Tal in the Himalayas. In 1952, he was posted to Ranchi TB Sanatorium branch as an assistant secretary.
In 1958, he was sent to Rangoon (Yangon) in Burma (now Myanmar) Sevashrama as its secretary.
He was elected a trustee of the Ramakrishna Math and member of the governing body of the Ramakrishna Mission in 1973.
In 1975, he was appointed an assistant general secretary of the twin organisations. Under his stewardship as relief secretary, the math and mission conducted massive relief and rehabilitation operations in various parts of India, Nepal and Bangladesh.
He became the general secretary of the math and mission in 1992 and remained at that post for five years till 1997 when he became a vice-president of the Order.
Swami Atmasthanandaji had travelled extensively all over the country and abroad and visited several branches of the Order and some unaffiliated centres spreading the messages of Ramakrishna, Sarada Devi, Swami Vivekananda and Vedanta, besides giving 'mantra diksha' to disciples.
He was one of the key persons to organise the Pallimangal (integrated rural development) activities in Kamarpukur and Jayrambati, a youth training centre at Saradapitha (Belur) and many other social service programmes.
Mamata Banerjee, who paid a visit to the ailing monk earlier in the afternoon, described his passing away as "an irreparable loss to the mankind".
"I paid my last visit to him this afternoon. A life of outstanding social & religious service. This is an irreparable loss to mankind," Banerjee said.
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