The prefecture hosts around half of the 50,000 troops and contractors in the country.
The sailor was attached to the United States 3rd Marine Division, which has a base in Okinawa.
The 32-year-old soldier and the 44-year-old woman, were found bleeding at the apartment on the southern Japanese island, a police spokesman said. The two were reportedly in a relationship, which ended with the sailor stabbing the woman to death before taking his own life. The child called a relative who contacted police.
U.S. Forces Japan says the Naval Criminal Investigative Service is working with local police to look into the deaths Saturday of a U.S. Navy sailor assigned to a marine unit, and an Okinawa resident.
Japan's vice foreign minister Takeo Akiba called US Ambassador to Japan William Hagerty Saturday, when he described the case as "extremely regrettable" and sought cooperation for the investigation, the ministry said in a statement.
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People there have long complained about crime, noise and the destruction of the environment as a outcome of the military presence.
Although Okinawa makes up less than 1 percent of Japan's land space, AP said, it hosts about half of the 54,000 American troops stationed in Japan, and is home to 64 percent of the land used by USA bases in the country.
United States service members have also been involved in a number of high-profile crimes against locals, fueling anti-American sentiment.
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Mr Potts continued: "At this time we do not believe that there is a relationship between the child or the family of the child". Potts did not offer details about his condition. "The child has been transported to the hospital and has been receiving care".
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