The US-led coalition fighting Islamic State described the attack on the headquarters as "unprovoked," but offered little information in its statement confirming the attack.
A number of Russian contractors were killed in US airstrikes on SAA portions in eastern Syria, according to local media.
No US troops embedded with the local fighters at their headquarters were believed to have been wounded or killed in the attack, the officials said, speaking on condition of anonymity.
The Pentagon says up to 100 pro-Assad troops were killed in the retaliation.
The international coalition is destroying many of the heavy machinery and weapons of the regime's forces in the east bank of the Euphrates River, according to a statement from the commander of the Derazur Military Council of the Association's militias.
The coalition did not disclose whether US troops had been present or involved in the retaliatory strike or offer any details on which forces attacked the Syrian Democratic Forces' headquarters.
A statement released by the Combined Joint Task Force said: "Syrian pro-regime forces initiated an unprovoked attack against well-established Syrian Democratic Forces headquarters February 7.
“Coalition service members in an advise, assist, and accompany capacity were co-located with SDF partners during the attack eight kilometres east of the agreed-upon Euphrates River deconfliction line.
“In defence of coalition and partner forces, the coalition conducted strikes against attacking forces to repel the act of aggression against partners engaged in the Global Coalition’s defeat ISIS mission.”
The Syrian army is backed by Iranian-backed militias and Russian forces.