(CNN) After a strong statement of protest by Japanese Prime Minister Shinzo Abe, President Barack Obama Wednesday expressed "his sincerest condolences and deepest regrets" for the murder of a Japanese woman allegedly at the hands of a former U.S. Marine.

Obama arrived in Japan Wednesday for a meeting of the G-7.

"The U.S. will continue to cooperate fully" and will continue to ensure "justice is done under the Japanese legal system," Obama said.

The two Presidents listen to their countries' national anthems during a welcoming ceremony at the Presidential Palace in Hanoi on May 23.

The two Presidents listen to their countries' national anthems during a welcoming ceremony at the Presidential Palace in Hanoi on May 23.

Obama holds a news conference with Vietnamese President Tran Dai Quang on May 23. Obama announced the United States is fully lifting the decades-long ban on the sale of military equipment to Vietnam. He said the removal of the ban was part of a deeper defense cooperation with the country and dismissed suggestions it was aimed at countering China's growing strength in the region.

Obama holds a news conference with Vietnamese President Tran Dai Quang on May 23. Obama announced the United States is fully lifting the decades-long ban on the sale of military equipment to Vietnam. He said the removal of the ban was part of a deeper defense cooperation with the country and dismissed suggestions it was aimed at countering China's growing strength in the region.

Obama, with Secretary of State John Kerry and other Cabinet members, attends a meeting with Vietnamese Prime Minister Nguyen Xuan Phuc, third from right, on May 23.

Obama, with Secretary of State John Kerry and other Cabinet members, attends a meeting with Vietnamese Prime Minister Nguyen Xuan Phuc, third from right, on May 23.

Obama walks to the left of Thi Kim Ngan, chairwoman of Vietnam's National Assembly, at the Presidential Palace in Hanoi on Monday, May 23.

Obama walks to the left of Thi Kim Ngan, chairwoman of Vietnam's National Assembly, at the Presidential Palace in Hanoi on Monday, May 23.

Obama delivers remarks at the National Convention Center in Hanoi on May 24. Obama made a forceful case for human rights in Vietnam and called for the "peaceful resolution" of disputes in the South China Sea.

Obama shakes hands with chef Anthony Bourdain in a shopping area of Hanoi on May 24. The President sat down with Bourdain to film a scene for CNN's "Parts Unknown."

Obama pays his respects during a visit to the Jade Pagoda in Ho Chi Minh City on May 24.

Obama pays his respects during a visit to the Jade Pagoda in Ho Chi Minh City on May 24.

Obama is greeted by U.S. Ambassador to Japan Caroline Kennedy and her husband, Edwin Arthur Schlossberg, at the airport in Tokoname, Japan, on May 25.

Obama is greeted by U.S. Ambassador to Japan Caroline Kennedy and her husband, Edwin Arthur Schlossberg, at the airport in Tokoname, Japan, on May 25.

U.S. President Barack Obama pauses for a translation during a bilateral meeting with Japanese Prime Minister Shinzo Abe in Shima, Japan, on Wednesday, May 25.

U.S. President Barack Obama pauses for a translation during a bilateral meeting with Japanese Prime Minister Shinzo Abe in Shima, Japan, on Wednesday, May 25.

From left: British Prime Minister David Cameron, Italian Prime Minister Matteo Renzi, U.S. President Barack Obama and Canadian Prime Minister Justin Trudeau talk together after a group photo session at the G7 summit in Shima, Japan, on May 26.

From left: British Prime Minister David Cameron, Italian Prime Minister Matteo Renzi, U.S. President Barack Obama and Canadian Prime Minister Justin Trudeau talk together after a group photo session at the G7 summit in Shima, Japan, on May 26.

World leaders join in a ceremony to plant trees at Ise Jingu shrine in Ise, Japan, on May 26. Obama and other major world leaders are in Japan for a Group of Seven, or G7, summit.

World leaders join in a ceremony to plant trees at Ise Jingu shrine in Ise, Japan, on May 26. Obama and other major world leaders are in Japan for a Group of Seven, or G7, summit.

From left: Italian Prime Minister Matteo Renzi, European Commission President Jean-Claude Juncker, French President François Hollande, Canadian Prime Minister Justin Trudeau, German Chancellor Angela Merkel, U.S. President Barack Obama, Japanese Prime Minister Shinzo Abe, European Council President Donald Tusk and British Prime Minister David Cameron walk past the Kagura-den as they visit Ise Jingu shrine in Ise, Japan, on Thursday, May 26. Obama is visiting Japan and Vietnam during his 10th trip to Asia.

President Obama greets members of the U.S. and Japanese military as he arrives at Marine Corps Air Station Iwakuni in Iwakuni on May 27.

President Obama greets members of the U.S. and Japanese military as he arrives at Marine Corps Air Station Iwakuni in Iwakuni on May 27.

Obama told U.S. and Japanese troops on May 27 at the Iwakuni Marine Corps Air Station in Iwakuni, Japan: "This afternoon I will visit Hiroshima. This is an opportunity to honor the memory of all those who were lost in World War II."

Obama told U.S. and Japanese troops on May 27 at the Iwakuni Marine Corps Air Station in Iwakuni, Japan: "This afternoon I will visit Hiroshima. This is an opportunity to honor the memory of all those who were lost in World War II."

President Barack Obama and Japanese Prime Minister Shinzo Abe shake hands after laying wreaths at the Hiroshima Peace Memorial Park in Hiroshima on Friday, May 27. Obama, the first sitting president to visit Hiroshima, called for a "world without nuclear weapons," during his speech but his remarks stopped short of an apology.

Kenneth Franklin Shinzato, a civilian worker at the U.S. Kadena Air Base in Okinawa Prefecture, was arrested on suspicion of abandoning the body of the 20-year-old woman.

The 32-year-old suspect also indicated that he killed the woman, who was reported missing last month, according to authorities.

"We want to see a crime like this prosecuted here in the same way that we would feel horrified and want to provide a sense of justice to a victim's family back in the U.S.," Obama said. "I think the Japanese people should know we are deeply moved and working with he Japanese government to prosecute not only this crime but prevent these kinds of crimes from happening again."

Abe said that he felt "profound resentment for this self-centered and despicable crime this case has shocked not just Okinawa but all of Japan."