Chinmoy died of a heart attack on Thursday at his home in New York. He was 76.
The Indian-born guru's body has been kept in an open casket in the meditation centre he had founded and named after him in Jamaica, Queens. His disciples and friends are pouring in from many parts of the world to pay their last respects.
A memorial service will be held on Monday, according to officials at the Sri Chinmoy Centre.
"Devotees are bringing flowers, they light candles, pray and meditate, creating great tranquility," Sanjay Rawal of the centre told IANS. The casket will be buried in the ground at the meditation centre in a couple of days, he said.
Many world figures who had known the guru have sent their tributes.
Soviet leader Mikhail Gorbachev said: "My long-time close friend Sri Chinmoy has passed away... he will forever remain a man who dedicated his whole life to peace."
Archbishop Desmond Tutu said in his message: "He worked tirelessly to bring different faiths together and inspired many to emulate."
The Archbishop had nominated Sri Chinmoy for the Nobel Peace Prize and Gorbachev had supported the nomination, according to the Sri Chinmoy Centre. Both are Nobel laureates themselves.
Among others who paid homage to Chinmoy were former US vice president Al Gore, the co-winner of this year's Nobel Peace Prize, Indian spiritual teacher Dada Vaswani and sitar maestro Ravi Shankar.
Vijay Nambiar, chief of staff to the UN secretary general, came personally to pay homage to the deceased.
Sri Chinmoy was a spiritual master who dedicated his life to inspiring and serving mankind. He inspired his followers to feats of extreme physical endurance.
Sri Chinmoy spent some years in the Aurobindo Ashram at Puducherry in south India, before coming to the US in 1964 to work in the Indian consulate.
As a spiritual guru, he did not create a mass following unlike some of his contemporaries. Instead, he tended to a small flock of dedicated disciples, numbering 7,000. They in turn set up over 100 Sri Chinmoy Centres across the world.
Since 1970 he used to lead 'Peace Meditation' at the UN headquarters for its staff and delegates to manifest what he called "the world body's inner meaning of love and oneness".
Better known outside India, Sri Chinmoy befriended world personalities including Mother Teresa, the Dalai Lama, Nelson Mandela and Princess Diana.
Prodigious and prolific, he wrote books, composed music, painted and gave concerts. He was also an avid athlete, attracting publicity for lifting humungous weights and well-known people.
He founded the World Harmony Run, the world's largest relay for peace involving tens of thousands of participants in over 70 nations.
Carl Lewis, winner of nine Olympic gold medals and spokesman for the World Harmony Run, said: "Sri Chinmoy's life was all about challenging yourself and being the best you can be. He's the reason I plan on running the New York marathon when I'm 50."