SEOUL, South Korea — North Korea said Wednesday that its leader, Kim Jong-un, had personally ordered the release of Jeffrey E. Fowle, an American, after considering requests from President Obama.

Mr. Fowle, an Ohio municipal worker and one of three Americans detained in North Korea, had been held for nearly six months before a United States military plane picked him up Tuesday. He arrived Wednesday in Ohio, where he was reunited with his wife and three children, who rushed to greet his plane when he arrived at Wright-Patterson Air Force Base near Dayton.

Mr. Kim recently reappeared in state-run news media after a six-week absence, ending widespread speculation about his health and his grip on power. With the statement on Wednesday, North Korea appeared to be burnishing Mr. Kim’s image at home as a leader capable of doing a favor for the American president.

Analysts also said the sudden release of Mr. Fowle might have been a conciliatory gesture from Mr. Kim to bolster his government’s efforts to engage Washington in a dialogue.