The Argentine was speaking aboard the papal plane on his way to Chile and Peru, the day after a false missile alert sparked panic in the US state of Hawaii, already on edge over fears of a North Korean attack.
Asked about the threat of nuclear war in the wake of a flurry of nuclear and missile tests since last year in North Korea, the pope said: "I think we are at the very edge.
"I am really afraid of this. One accident is enough to precipitate things," he told journalists.
The 81-year old, who has often spoken of the dangers of nuclear weapons, presented the press pack aboard his plane with a harrowing photograph taken in 1945 that shows a young Japanese boy carrying his dead brother.
The child, carried on the boy's back, was killed when the United States dropped a nuclear bomb on Nagasaki.
Francis had written on the back of the image just four words: "The fruit of war".
"I wanted to reprint and distribute it because an image like this can be more moving than a thousand words. That is why I wanted to share it with you," he said.