Separately, the US -led air and artillery strikes began overnight Wednesday in Deir al-Zour province.
Although Turkey has backed opposition troops since the Syrian conflict began in 2011, Ankara has moved closer to Assad's ally, Moscow.
Some 100 pro-regime forces were killed in the incident, according to the broadcaster.
The US maintains about 2,000 troops in Syria, who mostly work with the over 50,000-strong Syrian Democratic Forces, a mix of Kurdish and Arab fighters who have been the primary US-backed force fighting ISIS in Syria.
The river has always been a dividing line between USA -backed forces and Russian- or Iranian-backed fighters of the Assad regime. The US, however, has stated that it may remain in Syria indefinitely to counter what it describes as Iranian influence and to secure "post-Assad leadership" for the country.
IS had held most of Deir al-Zour since 2014.
It added that the coalition then "conducted strikes against attacking forces to repel the act of aggression against partners engaged in the Global Coalition's defeat-ISIS mission". The strikes were carried out in self-defence after the pro-Assad troops started firing artillery and tank rounds at the US-backed Syrian Democratic Forces, the United States military claimed.
The strikes inflicted what could be the largest number casualties that the coalition has exacted against the pro-regime forces.
The strikes came after the pro-regime militants initiated an attack against the headquarters of the Syrian Democratic Forces (SDF).
Regime forces were likely attempting to take an oilfield near Khusham.
The Omar oil field, one of the biggest in Syria, had a pre-war output of 30,000 barrels per day, while the Conoco gas field had a pre-war capacity of 13 million cubic metres a day.
The official said no coalition or USA personnel had been killed or wounded in the engagement but that one member of the SDF sustained injuries.
What does Syrian media say?Moscow's defense ministry said the USA was more interested in seizing Syrian economic assets rather than driving out the Islamic State Group from its last major stronghold.
An Al-Ikhbariyah TV correspondent said the bombing left "dozens of dead and wounded" and identified the pro-government fighters as "local people".
In a statement issued Thursday, the Russian Foreign Ministry said the United States military presence in Syria "poses a threat to the peace operation and menaces the unity of the country".