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Donald Trump speaks to a crowd at a rally in California.
In a tweet, the presumptive Republican presidential nominee criticized Obama for visiting the site while neglecting to mention the 1941 attack on Pearl Harbor.
"Does President Obama ever discuss the sneak attack on Pearl Harbor while he's in Japan? Thousands of American lives lost. #MDW," Trump wrote.
The country and top Japanese leaders have on numerous occasions expressed remorse for the nation's aggression in the lead-up to World War II.
Obama did not apologize for the US' decision to use nuclear weapons, but he was nonetheless rebuked by some conservatives for his decision to visit the nuclear memorial site at all.
In his speech, Obama criticized the colonial motivations that put Japan on the path to war with the US in the first place.
"The war grew out of the same base instinct for domination or conquest that had caused conflicts among the simplest tribes, an old pattern amplified by new capabilities and without new constraints," Obama said.
Obama also warned of the ability for mankind to "destroy itself" with nuclear weapons, and asserted that the world would be better off without them.
"We must have the courage to escape the logic of fear and pursue a world without them," Obama said of nuclear weapons.
He added: "We may not realize this goal in my lifetime, but persistent effort can roll back the possibility of catastrophe."
During his trip, Obama met with several survivors of the 1945 atomic bombing, who were children at the time. The final death toll from the attacks on Hiroshima and Nagasaki is estimated at just below 200,000 people, the majority of whom were civilians, as well as forced Korean laborers and a small number of American troops being held as prisoners of war.
Trump has been a critic of the close relationship between the US and Japan that has been rebuilt over the past three-plus decades. The presumptive Republican nominee has asserted that the Japanese - along with countries like Mexico, China, and South Korea - have unfairly benefited from globalization to America's detriment. He has also accused Japan of deliberately weakening its currency to stimulate exports.
More alarmingly to some US and Japanese foreign-policy experts, the real-estate magnate also suggested ending the decades-long strategic agreement between the US and Japan that allows the US to maintain bases in the Japanese archipelago in exchange for US military protection in the case of an attack on Japan.
As Foreign Policy has reported, most Americans are content with the state of the US-Japan relationship, though the relationship is less popular among Americans who identify as Republican.