Suu Kyi was speaking following a meeting in Myanmar's capital Naypyidaw at which Kono asked her to ensure the "safe and voluntary" resettlement of those who have fled, according to Japanese news agency Kyodo. They have been regarded by many majority Buddhists as illegal migrants from Bangladesh.
More than 600,000 Rohingya, who are not recognised by the Myanmar government as one of the country's many ethnic groups, have fled to Bangladesh since August a year ago, when violence between armed Rohingya and Myanmar security forces prompted a severe crackdown.
Meanwhile, a total of Dollars 71.2 million was received which is 85% of the request (USD 83.7 million) from donor global bodies and countries as an initial emergency response, the UNHCR said.
Saturday's report says Suu Kyi said: "It is a positive indication that we are taking the steps to be responsible".
The unrelenting Rohingya crackdown banished those hopes.
In response to Myanmar's military's admission of killing Rohingyas, Amnesty International said on Thursday that the confession is just the "tip of the iceberg".More news: Sako hands Palace narrow win over Burnley
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Joseph Tripura, a spokesman for the United Nations refugee agency UNHCR, said an investigation had been started.
ARSA, the Rohingya militant group, "wholeheartedly" welcomed the army's admission saying it validated the wider allegations of abuses including a campaign of rape and murder and the systematic torching of villages.
Police and a Red Crescent official said a candle sparked the fire late Thursday at a UN-run transit camp for refugees in Ghumdum border village.
Myanmar refutes the allegations, blaming militants for causing the violence and the global media and aid agencies for spreading false information due to a pro-Rohingya bias.
Rohingyas are a Muslim minority ethnic group in Myanmar.