Prime Minister Modi's first bilateral visit to Myanmar comes at a time when the Myanmarese government is facing international pressure over the 125,000 Rohingya refugees that have poured across the Bangladeshi border in just two weeks after Myanmar's military crackdown in the Rakhine state.
The prime minister, at a joint press statement with Ms Suu Kyi, also asserted that India stands by Myanmar amid the challenges the country is facing.
PM Modi and Ms Suu Kyi held talks and discussed ways to further cement the bilateral relations.
After the talks, Prime Minister Modi said India shares concerns over the violence in the Rakhine state where there has been a loss of innocent lives of people and military personnel.
Ms Suu Kyi, in her remarks, thanked India for taking a strong stand on the terror threat that Myanmar faced recently. She said that together India and Myanmar can ensure that terrorism is not allowed to take root on their soil or on the soil of neighbouring countries.
Hundreds have died since Rohingya militants raided police posts in Myanmar's Rakhine State last month.
UN Secretary-General Antonio Guterres has also called for the Muslims of Rakhine state to be given either nationality or legal status, and voiced concern about violence that has since late August forced nearly 125,000 people to flee and risk destabilising the region.