The Myanmar visit marks PM Modi's first bilateral visit to the neighbouring country.
Today, Modi focused on the need for the two countries to cooperate more deeply in securing their long and porous border - an emphasis Suu Kyi shared when she spoke.
India and Myanmar on Wednesday exchanged agreements between Election Commission of India and Union Election Commission of Myanmar.More news: Narendra Modi meets Myanmar's state counsellor Aung San Suu Kyi
Tens of thousands of Rohingya Muslims have fled Myanmar's Rakhine province following clashes with Buddhists and counter-terrorism operations by Myanmar's security forces.
A government statement said Suu Kyi told Erdogan that the Myanmar administration was "defending all the people in Rakhine in the best way possible".
"When it comes to finding a solution to a special issue, we hope that all stakeholders can work together towards finding a peaceful solution which while respecting the unity and territorial integrity of Myanmar", he said. In the meeting, the two leaders discussed ways to deepen India and Myanmar's "historical relationship". China wields influence with several of the militant groups that Suu Kyi has tried to bring to a dialogue with the government - giving it leverage in Myanmar's peace process that India can't match.More news: Unexploded WW-II bomb found in Frankfurt, 65000 residents evacuated
In the health care sector, the Foreign Secretary said India has upgraded three hospitals in Myanmar, including in Yangon and Sittwe.
She also mentioned images of killings posted on Twitter by Turkey's deputy prime minister, Mehmet Simsek, which he later deleted because they were not from Myanmar.
PM Modi's statement did not refer to Rohingya refugees but the BJP's national coalition in Delhi has already made it clear they were not welcome to India.More news: Italian Star Poses With Chelsea Shirt After Completing £23m Move
Modi arrived here on the second leg of his two-nation trip during which he travelled to southeastern Chinese city Xiamen where he attended the annual BRICS summit and held talks with Chinese President Xi Jinping, Russian President Vladimir Putin and other world leaders. Myanmar is one of India's strategic neighbours and shares a 1,640-km-long border with a number of northeastern states including militancy-hit Nagaland and Manipur.