The Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab militias fighting with the USA -led coalition, said six of its fighters had been wounded in the strike.
The Pentagon said earlier, military of the Syrian Democratic Forces, supported by the USA and its allies, were injured in a Russian air strike. Galloway says the man is being legally detained as a known enemy combatant.
US officials have previously said that roughly 250 people left the U.S.to join ISIS.
The U.S. citizen fighting with the Islamic State has reportedly been taken into custody.
The US-led Coalition told Rudaw English that as of Tuesday, SDF partner forces "have liberated approximately 42,000 square-kilometers in Syria" which is estimated to be "77 percent of the territory previously held by ISIS". According to the Daily Beast, he was captured; according to spokespeople for the USA military, he "surrendered". But a spokesman for the US-led coalition told reporters Thursday that the SDF would not enter the city, seemingly ensuring that the Russian-backed pro-regime troops would be the ones to capture it.
A State Department official told CNN that it was aware of the reports but had "no information to share at this time", while the Justice Department and Federal Bureau of Investigation also declined the network's request for comment.
The American fighter, whose identity was not released, is not the first American ISIS fighter captured on the battlefield.
The loyalists of the Islamic State of Iraq and Syria (ISIS) terrorist group in Afghanistan, ISIS Khosan, have beheaded two civilians on espionage charges in eastern Kunar province.
In March 2016, Mohamad Jamal Khweis of Virginia was captured by Kurdish forces in Iraq after he changed his mind and fled Mosul.
A US official told ABC News that the individual is still overseas, as the Department of Justice and the Trump administration determine how to move forward. He was brought to the US for a trial and convicted in June of providing material support to ISIS.
Although Trump said during his presidential campaign that he would be "fine" with sending USA citizens captured on the terrorism battlefield to the US detention facility at Guantanamo Bay, Cuba, to be tried by military commissions, such proceedings are, by statute, authorized only for foreigners.