Joo Won-Moon, 21, who attends New York University and has permanent US residency, said he had hoped to create an "event" that could improve relations between North and South Korea.
It was unclear whether he was speaking freely or had been told by North Korean authorities what to say.
"I wanted to be arrested," Joo told a CNN reporter, looking relaxed and even smiling as he walked into a conference room at Pyongyang's Koryo Hotel for the interview.
He told CNN he had crossed two barbed-wire fences and walked through farmland until he reached a large river. He followed the river until soldiers arrested him.
"I thought that by my entrance to the DPRK (North Korea), illegally I acknowledge, I thought that some great event could happen and hopefully that event could have a good effect on the relations between the North and (South Korea)," Joo said, without elaborating on the event.
Joo was born in Seoul, moved to Wisconsin with his family in 2001 and then moved again to Rhode Island.
He said he understood that his parents were worried about him but he was being well treated.
He told CNN he had not yet been informed what charges he might face but was being held in very comfortable conditions.
KCNA said Joo had admitted that his illegal entry was a "serious violation" and added that his case was under investigation.
CNN also interviewed on Sunday two other South Koreans being held in the North on espionage charges.
Both Kim Kuk-Gi, a Christian missionary, and Choe Chun-Gil, a businessman, admitted spying for Seoul in the interviews in Pyongyang in the presence of North Korean minders.
The two claimed they had not been coerced or coached on what to say. CNN noted that their accounts were "strikingly similar".
Foreigners arrested in North Korea have previously admitted wrongdoing on camera or in writing, only to retract their statements following their return home.
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