The minister also said that the probe into the incident was still ongoing and sent condolences to the victim's family.
On Saturday, Japanese Vice Minister of Foreign Affairs Takeo Akiba urged US Ambassador in Tokyo William Hagerty to express protest over the murder of an Okinawan woman by a US serviceman.
A 32-year-old serviceman from the US Marine Corps is believed to have stabbed his 44-year-old Japanese girlfriend to death before killing himself at their apartment in the town of Chatan near the US base earlier this month.
Japan asked the US envoy to take efforts to prevent a recurrence.
Many Okinawans oppose the presence of US troops on the small Pacific island due to associated crimes, noise and environmental damage.
The southernmost Japanese prefecture hosts around a half of 50,000 US troops and contractors in the country.