Singh held vast political power within the leftist party until 2010, when he left the bloc to become an independent politician.
He was later elected as a member of parliament for Rajya Sabha in India by voters in Uttar Pradesh.
Indian political spectrum leaders paid tribute to him on Saturday.
“Amar Singh Ji was an energetic public figure,” Modi wrote. “Over the past few decades he has witnessed some of the major political developments up close. He was known for his friendships in many areas of life. Sad about his disappearance. “
Singh had struggled with health issues for several years, but continued to post on his Twitter page, celebrating Eid and paying tribute to revolutionary fighter Bal Gangadhar Tilak hours before his death.