The Myanmar visit marks PM Modi's first bilateral visit to the neighbouring country.
Modi announced free visas for Myanmar nationals keen to visit India, standing next to Suu Kyi - the country's State Counsellor and de-facto leader - in Nay Pyi Taw, at a time his administration has declared plans to deport 40,000 illegal Rohingya refugees now in India.
Naming Mahatma Gandhi, Bal Gangadhar Tilak, Rabindranath Tagore and Bahadur Shah Zafar, he said Myanmar had become the "second home" for those who had to leave their own homes during the freedom struggle.
The two leaders discussed the security situation prevailing along their borders and expressed concern at various incidents of terrorism and extremist-inspired violence that have taken place in their countries.More news: Are Analysts Bearish NEXT plc (LON:NXT) After Last Week?
India and Myanmar signed 11 agreements in a range of sectors, including one on maritime security cooperation, to further strengthen their multifaceted partnership.
In the statement, he said India shares Myanmar's concerns over "extremist violence" in the Rakhine state, especially the loss of innocent lives.
State Councillor Aung San Suu Kyi said, "There are many areas in which we can cooperate".
In the health care sector, the Foreign Secretary said India has upgraded three hospitals in Myanmar, including in Yangon and Sittwe.More news: 'Dancing with the Stars' cast includes Nick and Vanessa Lachey, Jordan Fisher
Myanmar condemned the recent terror attacks during the Amarnath Yatra in India as also various acts of terror perpetrated by terrorists from across the borders. The Prime Minister had in the meantime visited every other neighbour - except the politically unstable Maldives - for bilateral meetings.
Today, he met Suu Kyi - who effectively heads the government though she can't legally because of a constitutional provision - for talks that were critical for India to try and reassert New Delhi's commitment to the relationship, officials said.
Some Western critics have suggested the Nobel Peace Prize she won in 1991 as a champion of democracy be revoked.
"India's democratic experience is relevant to Myanmar". The Prime Minister had visited the country back in 2014 to attend the ASEAN-India Summit.More news: White House: Trump will donate $1M to Harvey relief