Marzuki Darusman decried stepped-up violence in Myanmar over the last month that has caused more than 400,000 people to flee, and asked the United Nations -backed Human Rights Council for a six-month extension until next September for his team's first written report.
"There has been a call for the repatriation of refugees who have fled from Myanmar to Bangladesh", she said.
Violence erupted on August 25 when a group of Rohingya militants torched police checkpoints in Rakhine.
"They looted our house, then marched us with more than a hundred of our neighbours to a secluded spot", she told the Dhaka Tribune.
Suu Kyi in her speech said, "50% of the villages of Muslims are intact".
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In her speech, Suu Kyi, the Nobel Peace Prize victor for her non-violent resistance to the military junta that used to rule Myanmar, did not mention the Rohingya specifically and only used the term in reference to the "Rohingya Salvation Army".
Though members of the long-persecuted religious minority first arrived in the western state of Rakhine generations ago, most people in Myanmar consider them to have migrated illegally from Bangladesh.
At its March session, the council agreed to "dispatch urgently" a fact-finding mission to look into alleged human rights violations and abuses by the military and security forces, particularly in Rakhine state where many Rohingya live.
Suu Kyi's pledge to repatriate the refugees "is new and significant", said Richard Horsey, an independent analyst based in Myanmar, explaining it would in principle allow for the return of those who can prove residence in Myanmar-rather than citizenship.
Nyan Win, a central executive committee of the ruling National League for Democracy party, said as there are thousands of refugees in Bangladesh they need documents of their refugee status from Myanmar to accept them.
In an address timed to pre-empt likely censure at the UN General Assembly in NY, she said Myanmar stood ready "at any time" to repatriate refugees in accordance with a "verification" process agreed with Bangladesh in the early 1990s.
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More than 410,000 Rohingya have fled to Bangladesh since August 25 when the Arakan Rohingya Salvation Army attacked police posts and an army base that led to military clearance operations in the conflict-stricken region.
"Aung San Suu Kyi's claims that her government "does not fear worldwide scrutiny" ring hollow".
Following the speech, she held a two-hour closed-door meeting with global diplomats who she has invited to visit Rakhine provided security is deemed to be sufficient to "see for yourselves". If what she said is not a lie then let the world media in, so that they can see whether we are tortured or we are happy.
"A verification process was set up as early as 1993", she said.
The rights group blasted Suu Kyi for remaining "silent about the role of the security forces", whom they have accused of being "engaged in a campaign of ethnic cleansing".
Britain is among the countries that have urged Myanmar's political leader, Aung San Suu Kyi, to halt the violence against the Muslim minority group. So many people have died over the years and she has done nothing.
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The claims emerged during a petition hearing at India's supreme court filed on behalf of two Rohingya refugees challenging a government decision to deport the ethnic group from India.