Singh, the first Indian Prime Minister to visit Myanmar in the quarter of a century, and Suu Kyi held discussions for 45 minutes.
During their meeting which took place on the last day of the Prime Minister's historic visit, Singh handed over to the Nobel laureate an invitation from Sonia Gandhi to visit India to deliver the next Jawaharlal Nehru memorial lecture.
Accepting in principle the invite, Suu Kyi said, "I hope I will be able to take up the invitation not before too long".
Emerging from the meeting at the Sedonia Hotel, where the 66-year-old opposition leader of Myanmar called on the Prime Minister by sticking to protocol, Suu Kyi recalled the close association she and her parents had with Pandit Jawaharlal Nehru and his family.
"India and Burma have been friends not only because of geographical proximity but also because of shared values, heritage and fight for independence," she said.
Speaking first, the Prime Minister paid rich compliments to Suu Kyi, saying her "struggle and her determination have inspired millions of people all over the world".
"We in India are very proud of the very long-standing association with her (Suu Kyi) and the members of her family," Singh said.