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".
Winter storm is moving in - The amount of snow and ice expected
Rain will turn to a mix of freezing rain, sleet and eventually light snow this evening and continue until early morning Friday . Gusty winds are possible in wind prone areas producing localized blowing and drifting snow and reduced visibility.
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.
4 flu-related deaths in the state, including 1 in Middle Georgia
William Beaumont Army Medical Center encourages people to protect themselves and their loved ones by getting the flu shot now. The lone flu death in Marin County this year involved a person under 65, and it's not known if the person was vaccinated.
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.
West Ham fans delighted with winger's display against Huddersfield: "Unreal", "Superb"
Nothing that we like but something that can always happen when you're human. "We made too many easy mistakes which you can't do at this level".
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.