"I want to express on a personal level how deeply honoured I am, how deeply moved I am" to be the first US secretary of state to visit the memorial, he told reporters after his visit during a G7 meeting in the Japanese city.
He described the memorial as "extraordinary" and called it a "gut-wrenching display that tugs at all your sensibilities as a human being".
Kerry was the highest-ranking US administration official to pay respects at the spot where American planes launched the world's first nuclear attack, in 1945.
The atomic bombing of Nagasaki followed three days later and Japan surrendered within a week, ending World War II.
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"Everyone should visit Hiroshima, and everyone means everyone," Kerry said.
"I hope one day the president of the United States will be among the everyone who is able to come here," he added.
But he declined to elaborate on whether such a visit - it would be a first by a sitting US president - was likely.
"Whether or not he can come as president, I don't know. That is subject to a very full and complicated schedule that the president has to plan out way ahead of time."
Kerry visited the memorial with other Group of Seven foreign ministers who were wrapping up a two-day meeting in Hiroshima to prepare for the summit.
That meeting will take place in a different region of the country. But speculation has risen that Obama, who has called for a world free of nuclear weapons, could journey to Hiroshima.