If the report of airstrikes against the SDF this time around are true, it would mark the second time in a week that the Russians hit the US -backed militia.
Asapov has been described as one of the senior Russian military advisers in Syria.
The Russian Defense Ministry said a day earlier that Lieutenant General Valery Asapov had been killing amid shelling near the city of Deir al-Zor.
Russia's Defence Ministry subsequently said the waters of the Euphrates had risen as soon as the Syrian army began crossing it, suggesting this could only have happened if upstream dams held by the USA -backed opposition had been opened.
In recognition of his services, Asapov will be presented with a posthumous state decoration.
Brig. Gen. Talal Silo, also from the SDF, stated that the firefight killed 65 ISIS militants, while 100 others surrendered.
On September 16, the SDF said a Russian air strike wounded six of its fighters, but Russia denied carrying out the attack.
The main U.S-backed Syrian force fighting the Islamic State group says a Russian airstrike on a gas field it recently captured from the extremists killed one of its fighters.More news: OPEC Keeps Oil Market Guessing Over Further Action on Cuts
Though they have a common enemy in IS, the SDF and Assad's forces disagree on key areas and are backed by rival worldwide powers.
Lavrov said any action by the US -backed SDF forces that would "make it difficult" for Assad's troops to liberate Deir Ez-Zor from ISIS "would not be tolerated".
Facing no resistance of the ISIS militants, the #SDF units are advancing along the left shore of the Euphrates towards Deir ez-Zor.
While both oppose Islamic State (IS), they are engaged, via proxies, in a race for strategic influence and potential resources in the form of oilfields in eastern Syria's Deir al-Zor province.
According to Russia's Defence Ministry, Russia lost ten people in Syria in 2017.
The Conoco field is named for the American company that discovered the gas reserves and built a processing plant there. The U.S. -led coalition said it could not confirm who carried out the strike.
"We will not stand by with our arms crossed and we will use our legitimate right to self-defence", said the statement by the SDF, which fights alongside the USA -led coalition.