Mr Trump and Japanese Prime Minister Shinzo Abe met on Monday at the Akasaka Palace.
Trump referenced North Korea's recent nuclear activity ahead of a meeting later on Monday with the families of Japanese citizens who were abducted by North Korea decades ago, to train North Korean spies in Japanese language and customs.
North Korea has admitted kidnapping 13 Japanese citizens in the 1970s and 80s, and returned five to Japan in 2002. It maintains the rest are dead - something Japan does not believe.
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