The official, who spoke on condition of anonymity because he was not authorized to discuss the situation, said the man is being held by the Haqqani network, a family-run militant group that operates along the Afghanistan-Pakistan border.
The official would not discuss the man's identity or the circumstances of his capture. The incident was first reported Wednesday by the Daily Beast web site.
The FBI, the White House and the man's wife have urged public officials and media organizations not to discuss the matter publicly, the official said.
The department is "aware of reports that an American is being held," spokesman Mark Toner said, and "we reiterate our calls for US citizens being held hostage around the world to be released."
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On Monday, Rep Duncan Hunter, a Republican, who has been critical of US hostage recovery efforts, wrote a letter to President Obama urging that he appoint a federal hostage coordinator.
In the letter, he noted that "there are still Americans in captivity in the Afghanistan-Pakistan region."
The only other known American captive there is Caitlin Coleman, who was kidnapped along with her husband, Canadian Joshua Boyle, while traveling in Afghanistan in 2012. American officials call the Haqqani network a terrorist organization and have targeted its leaders with drone strikes.