The meeting between Singh and Suu Kyi, held after the 3rd BIMSTEC Summit, was warm and cordial, officials said.
Suu Kyi is a Nobel laureate and the chairperson and secretary general of the opposition party National League for Democracy.
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Suu Kyi, 68, who has studied at New Delhi's Lady Shri Ram College, came to India in 2012 on the invitation of UPA Chairperson Sonia Gandhi to deliver the Jawaharlal Nehru Memorial Lecture.
Suu Kyi spent several years in India during her early days when her mother Daw Khin Yi was Ambassador to the country.
She was freed in 2010 after being kept in house arrest in Myanmar for years by the military junta.