According to news report, Kono made the comments in a joint news conference with Myanmar's de facto, leader Aung San Suu Kyi, in the capital Naypyitaw.
The request comes after Myanmar military admitted that some of its soldiers were involved in the murder of 10 captured Rohingya men in western Rakhine state in September a year ago and buried them in a mass grave near Inn Din village in Maungdaw township.
Aung San Suu Kyi stressed the importance of the rule of law and said the military would take responsibility. She added: "I believe our investigation will prevent such things from happening again".
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Kono arrived in Rakhine state on board a Myanmar military helicopter on Saturday as the first minister from a foreign country to visit the region.
United Nations High Commissioner for Human Rights Zeid bin Ra'ad Zeid al-Hussein had decribed the offensive - that led to the exodus of around 650,000 Rohingyas to neighboring Bangladesh - as ethnic cleansing.
Hundreds of thousands of the Rohingya have fled to neighboring Bangladesh since fighting broke out between Rohingya militants and security forces previous year.
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On Wednesday the military acknowledged that security forces and villagers were responsible for the deaths of 10 people found in a mass grave in December.
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. They have been regarded by many majority Buddhists as illegal migrants from Bangladesh.
Suu Kyi rarely speaks to the media and has said little in public about the crisis in the western state.
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The Japanese foreign minister said Tokyo, one of Myanmar's biggest foreign aid donors, planned to give about $20 million for humanitarian support to Rohingya refugees, subject to parliamentary approval, Kyodo said.