The casualty in Syria marks the first time an American soldier has been injured in that country since military advisors deployed there at the end of last year.
Pentagon spokesman Captain Jeff Davis said the soldier was wounded by “indirect fire” — a term that typically refers to rocket or artillery fire — north of Raqa, the jihadists’ de facto capital.
The Iraqi incident occurred near in northern Iraq near the city of Erbil, also by indirect fire, Davis said.
He stressed the troops was “not on the front line” and “were not engaged in active combat.”
But Defense Secretary Ashton Carter later told reporters that “of course” the troops were in fact in combat.
President Barack Obama has repeatedly assured the American public there would be no US combat boots on the ground in Iraq or Syria, but troops are edging ever closer to the front lines, leading many to question what constitutes “combat” versus simply advising local partner forces.
The United States has sent more than 200 special forces personnel to northeastern Syria to advise and assist rebels fighting the Islamic State group.
American soldiers are focusing on aiding the Syrian Democratic Forces, a coalition dominated by the Kurdish militia YPG.
Fighting is currently raging in northern Raqa eight days after the start of an SDF offensive, with support from air strikes by a US-led international coalition.