Syrian state-run television reported on Thursday that the 33-year-old Michigan woman, identified as Nicole Lynn Mansfield, and the two others were members of al-Qaeda-linked al-Nusra Front.
They were ambushed by Syrian government forces in their car while traveling through Idlib.
Television footage showed a black car riddled with bullets, and three bodies laid out with multiple gunshot wounds.
It also showed a cache of weapons, a computer, a hand-drawn map of a government installation, and a flag belonging to the terrorist group al-Nusra Front.
Mansfield’s family members say two FBI agents interviewed them and confirmed to them reports on her death.
Syria has been gripped by deadly unrest since March 2011, and many people, including large numbers of government forces, have been killed in the violence.
Damascus says the chaos is being orchestrated from outside the country, and there are reports that a very large number of the militants are foreign nationals.
The Syrian government says the West and its regional allies including Qatar, Saudi Arabia, and Turkey are supporting the militants.
Several international human rights organizations have accused militants operating in Syria of committing war crimes.