TOKYO — The US military imposed a curfew on Friday on all of its nearly 50,000 uniformed personnel stationed in Japan, as it tried to respond to outrage over the suspected rape of a woman on Okinawa by two American sailors.

The commander of US forces in Japan, Lieutenant General Salvatore Angelella, apologized for the case, saying that US military personnel will also be required to take ‘‘core values training.’’ Earlier Friday, the US ambassador to Japan told the Japanese defense minister and the governor of Okinawa that the United States would cooperate ‘‘in every way possible’’ with the investigation of the two sailors, who are in Japanese custody.