"Human rights violations and all other acts that impair stability and harmony and undermine the rule of law will be addressed in accordance with strict laws and justice", Suu Kyi said in Myanmar's capital, Naypyidaw, in her first speech since recent violence erupted in the country's northern Rakhine state.
More than 400,000 members of Myanmar's Rohingya minority have fled fighting in Rakhine state, amid what rights activists and some world leaders have alleged is a military-led campaign of "ethnic cleansing".
In her nationwide address, Suu Kyi insisted that army "clearance operations" in response to attacks by Rohingya militants had finished on September 5 and denied that Rakhine was in flames.
"We invite you to join us, to talk to us, to discuss with us, to go with us to the problem areas, where we can guarantee security for you", she said.
"We are concerned to hear that numbers of Muslims are fleeing across the border to Bangladesh", she said, adding, "We want to find out why this exodus is happening".More news: Knife-wielding United States student shot dead
We don't want Myanmar to be a nation divided by religious beliefs or ethnicity.
"There have been allegations and counter allegations, will listen to all, culprits will be punished irrespective of race or religion", Suu Kyi said. "That is one of the things we agreed on", he said.
"We have to make sure these allegations are based on solid evidence before we take action". Despite her ambition to become the nation's president, Myanmar's current constitution bars her from presidency because her two sons are United Kingdom citizens and she is a widow, which makes her not eligible.
The leader said she nevertheless wanted the global community to know what was being done by her government.
Suu Kyi, 72, is banned from the presidency by the military-drafted constitution because her children have British citizenship. Her only comment on the situation saw her lash out at a "huge iceberg of misinformation" that she said was leading to a distorted view on the crisis in the rest of the world. "We have seen too many vulnerable people having to flee for their lives".
Suu Kyi said on Tuesday that Myanmar stood ready "at any time" to verify the status of those who have fled to Bangladesh to aid the return of those eligible for resettlement.
India on Tuesday argued that socio-economic development projects are only long-term solution for the problems of violence-hit Rakhine state in Myanmar.