Media and television reports described it as a traditional courtesy meeting extended by an incumbent Prime Minister on the previous occupant of the august office.
Dr. Singh and his wife Gursharan Kaur personally received Prime Minister Modi in the portico of the residence before going into the residence for talks.
Since the morning, Modi has met leaders from Afghanistan, Maldives, Sri Lanka, Bhutan, Mauritus, Nepal and Pakistan.
Modi had a nearly hour-long bilateral meeting with the Prime Minister of Pakistan, Nawaz Sharif. What transpired between the two leaders during their meeting on Tuesday afternoon was not known.
Modi started his day by assuming charge at the Prime Minister's Office (PMO).
Narendra Modi was administered oath of office and secrecy by President Pranab Mukherjee as India's 15th Prime Minister along with his 44-member Cabinet on Monday evening.