"I have no words to express, considering how the family feels," Prime Minister Shinzo Abe told reporters. "We urge the US side to take thorough measures to prevent the recurrence of such events."
The arrest sparked outrage on Okinawa, where anti-US military sentiment is high because of a heavy American troop presence. It could fuel further opposition to the relocation of a US Marine Corps air station on the southern Japanese island, a long-delayed project that Abe has been trying to push forward in the face of large protests.
Investigators determined that the body is that of a 20-year-old woman missing since April 28, when she messaged her boyfriend that she was going for a walk.
Police said they suspect Shinzato was also responsible for her death. He has not been charged.
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In Washington, Defense Department spokesman Peter Cook said the man arrested was a US military contractor. "This is an appalling tragedy," he said. The US military extends its "deepest sympathies to the people of Japan, and express our gratitude for the trust that they place in our bilateral alliance and the American people."
Okinawa Governor Takeshi Onaga said he was "outraged" and that the death of the woman broke his heart. "As I look back at all the developments to date, I'm simply speechless," he said.
Onaga has spearheaded opposition to the relocation of US Marine Corps Air Station Futenma from a densely populated neighborhood in central Okinawa to another site on the island, saying the facility should be moved away from Okinawa instead.
Okinawa is home to more than half of about 50,000 American troops based in Japan. Many Okinawans complain about crime and noise connected to the bases.