Russian media said Russian private contractors and pro-government forces advanced on oil fields in the eastern Deir el-Zour province and were targeted by the United States.
Even as the Kremlin denies any official link to them, scores of Russian mercenaries wounded in USA strikes in Syria are being treated at Defense Ministry hospitals.
Already Grigory Yavlinsky, a veteran liberal politician who is running for president in elections next month, has called on Putin to disclose how many Russians had been killed in Syria and in what circumstances.
Lieutenant General Jeffrey Harrigian, who heads up Air Force operations for the region, told Pentagon reporters: "We detected and saw a tank that took a shot at us". The attack was reportedly called for by the Syrian Democratic Forces (SDF) militia and lasted for about four hours.
Russian Federation also denies having personnel in the area.
Russian forces are supporting the Syrian government in the fight against opposition groups, some of which are backed by the United States, and elements of both sides are fighting the last remnants of the Islamic State group in Syria. However, it is possible that the Russian military was not aware of the attack planned by the Russian contract soldiers acting on orders of the Assad regime.
Harrigian said the attack by the pro-Assad forces was not a surprise since the US and its partners had observed them engaged in a slow buildup the week before the attack.
Mercenaries, who've been active in the conflicts in eastern Ukraine and Syria, allow Russian Federation to deny official involvement in operations when things go wrong.
Kremlin spokesman Dmitry Peskov declined to comment on the incident, in which the death toll of private Russian soldiers may have been five times greater than the Russian Defense Ministry's official count of servicemen who have died in Syria.
Their target was a base of the US-backed Syrian Democratic Forces, which came under artillery fire.
But analysts believe Russian Federation is using so-called private security firms to avoid deaths among its conscript army which could prove unpopular with its citizens - especially in the year of its presidential election.
Mr Yavlinsky said fierce mercenary forces "are trained at Russian army facilities" and "receive military awards in the Kremlin" in secret.
It remains unknown who was paying the Russian fighters, whether it was Russia itself, Syria, or Iran. Hassan told The Washington Post's David Ignatius that he called his regular Russian liaison contact in Deir el-Zour, hoping to avoid a battle with the advancing unit. US officials also said the Russian government had lodged no complaint about its citizens being killed.
Moscow launched a military operation in Syria in support of President Assad on 30 September 2015.
Yury Barmin, a Middle East analyst at the Russian International Affairs Council, a think tank set up by the Kremlin, said Russia supports Assad's efforts to reclaim the "crucial" eastern region of Deir Ezzor to help fund his national reconstruction and reconciliation plan, which the US opposes.
Russian media say an unknown number of private Russian military contractors have been killed by a USA strike on a government base in Syria.