One of the prisoners had been cleared for release in recent days only to have that decision reversed by members of the Houthi rebellion that toppled the U.S.-backed government earlier this year and now controls most levers of power in Yemen.

The Americans are believed to be held at a prison in Sanaa, the Yemeni capital, which has been bombed repeatedly as part of an air campaign led by Saudi Arabia aimed at dislodging the Houthis from power. The United States has provided intelligence support to that operation.

The detention of the Americans has complicated U.S. efforts to navigate the chaotic aftermath of the Houthi takeover, which displaced a government that had cooperated extensively with the United States on drone strikes and other counterterrorism operations against a dangerous al-Qaeda affiliate in the country.