"Australia must do whatever we can to support those who have fled and who cannot return home".
The exodus of refugees was triggered by the military's response to attacks by Muslim militants in Rakhine state on August 25.
However, Suu Kyi did acknowledge that an "exodus" was indeed occurring.
Almost 40,000 Rohingyas have taken refuge in India.
On September 16, the United Nations placed the total number of Rohingya Muslims who had fled to Bangladesh at 4,09,000 since violence erupted in Rakhine state on August 25.
Journalism takes a lot of time, money and hard work to produce, despite all the hardships we still do it, because we believe our perspective matters - because it might well be your perspective, too.
"We are a young and fragile country facing many problems, but we have to cope with them all..."
On reports that Rohingya villages have been burned down by security forces, Suu Kyi said: "There are allegations and counter-allegations and we have to listen to all of them". We have to make sure those allegations are based on solid evidence before we take action.
".We are here at the Obra Spot in Circle to begin a procession to Accra which is the Art centre where some of us will leave and go to the Isreali Embassy to deliver a petition".
"There has been a call for the repatriation of refugees who have fled from Myanmar to Bangladesh".
"We are prepared to start the verification process at any time", Suu Kyi told diplomats gathered in the capital Naypyidaw in a nationally televised speech in English.
Bangladesh has given a "note verbale " to the Myanmar High Commissioner's office in Dhaka regarding use of land mines at the border between the two nations to prevent the Rohingyas from moving into Bangladesh. "Invite members of the global community to visit", said Suu Kyi.
There are acute shortages of almost all forms of aid, with many Rohingyas huddling under tarps as their only protection from monsoon rains. The government must also urgently allow humanitarian actors full and unfettered access to all areas and people in need in the region. But we would like our friends to join or endeavour.
Opposition foreign affairs spokeswoman Penny Wong acknowledged there would be some disappointment over what Ms Ms Suu Kyi did and didn't say.
The army loosened its monopoly on power in 2011 but has retained control of security policy and other key branches of government.