A Colombian police general said Kevin Scott Sutay, 26, had entered a hot zone against warnings.
The rebels offered to free Sutay as a good-faith gesture in announcing on their website Friday night that he was in their custody.
The Revolutionary Armed Forces of Colombia, or FARC, said Sutay had described himself as a 2010-11 veteran of the Afghan conflict who left the armed forces in March.
U.S. Ambassador Michael McKinley denied that and also said Sutay was not an active member of the military.
"We understand that (he) was on a trip as a private citizen through Latin America," the ambassador told reporters when questioned about Sutay after attending a Mass marking Colombia's independence day.
"He is a citizen who has nothing to do with Colombia's internal conflict."
The chief of Colombia's anti-kidnapping police, Gen Humberto Guatibonza, told The Associated Press that Sutay had spent from June 11-13 in the Las Palmas hotel in San Jose del Guaviare, where a Colombian military base is located, then attempted land travel to Puerto Inirida, capital of the eastern state of Guainia on Venezuela's border.
He described Sutay as a thin, tall man with a military-style haircut .
Hotel officials and police told him "the area was dangerous," said Guatibonza, but he ignored them. He said local anti-kidnapping police had him sign a statement saying he took responsibility for his action.
The FARC has three active fronts in the region and said it captured Sutay on June 20 in the nearby town of Retorno.
The Pentagon yesterday referred queries about Sutay's military background to the U.S. State Department and the embassy in Bogota. An embassy spokeswoman, Erika Avila, said she had no additional information to offer.
