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.
Myanmar's leader Aung San Suu Kyi said on Friday it was "positive" that the country's military was taking responsibility for the actions of troops, after the army said soldiers were involved in killing 10 captured Rohingya Muslims.
"It is true that both the villagers and security forces admitted they killed the 10 Bengali terrorists", the military statement added, "The army will take charge of those who are responsible for the killings and who broke the rules of engagement".
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 past year, when violence between armed Rohingya and Myanmar security forces prompted a severe crackdown.
Burma's state-run media said on Wednesday that authorities have started the land work to construct buildings to accommodate returned refugees from Bangladesh in northern Rakhine, where refugees will be temporarily placed after their citizenship is scrutinised.
"More than 650,000 Rohingya have fled Rakhine since a military crackdown launched in August 2017, " it reported.
"Japan wants to actively support Myanmar's efforts", Kyodo quoted Kono as telling the news conference.
Myanmar and Bangladesh signed an agreement on the repatriation of Rohingya refugees on 23 November, and Myanmar, said it would start the process by 23 January.
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.