The man was apprehended yesterday night while lying on a bank of the Han River in a restricted military area near the border, said the official, who spoke on condition of anonymity due to office policy.
The man told investigators that he tried to go to North Korea to meet leader Kim Jong Un, South Korea's Yonhap news agency reported, citing an unidentified government source. It said the man, aged around 29, is a computer repairman from Texas who came to South Korea 10 days ago.
Americans are occasionally arrested after entering North Korea illegally from China, but a US citizen trying to get in from South Korea is unusual.
In the 1960s, several US soldiers walked into North Korea while on a patrol near the mine-strewn Demilitarized Zone, or DMZ. Those army deserters later appeared in North Korean propaganda films and taught English there.
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In 1996, American Evan C Hunziker entered North Korea by swimming across the Yalu River that marks the Chinese border. Hunziker, who apparently made the swim on a drunken dare, was accused of spying and detained for three months.
About 27,000 North Koreans have defected to South Korea to avoid poverty and political suppression since the end of the Korean War. Some South Koreans have attempted to defect to the impoverished, authoritarian North, but such cases are rare.
Last year, South Korean soldiers shot and killed a man with a South Korean passport who officials said ignored warnings while swimming across the Imjin River toward North Korea.