Gen Nakatani's visit to the island comes just days before a high-profile trip to Japan by US President Barack Obama.
"I deliver a strong message of regret and at the same time make a protest," Nakatani told US military commander Lt. Gen. Lawrence Nicholson, according to public broadcaster NHK, as he demanded the US military in Okinawa ensure discipline among troops.
For his part Nicholson told Nakatani: "Our heartfelt prayers and condolences are offered to the family."
Okinawan police arrested Kenneth Franklin Shinzato on Thursday for allegedly disposing of the woman's body in a weed-covered area in southern Okinawa.
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The man, a US citizen and former US Marine, who works at the US Kadena Air Base, has reportedly admitted to raping and killing 20-year-old Rina Shimabukuro, who had been missing since late April.
Prime Minister Shinzo Abe on Friday expressed "outrage" after the arrest, while Foreign Minister Fumio Kishida summoned US ambassador Caroline Kennedy to lodge a protest, calling the case "very cruel and atrocious".
The Hiroshima visit by Obama, who has a record of calling for global denuclearisation, has been well received in Japan but the issue of the heavy US military presence on Okinawa has long been a periodic thorn in the side of relations.
More than half of the 47,000 US military personnel in the country are stationed there, and rapes and other crimes by service personnel have sparked local protests in the past.
But continued crimes by American personnel remain a potent rallying point for Okinawans and others in Japan who oppose the presence of the bases on the crowded island, where pacifist sentiment runs high.