At least two Russian fighters were killed in US air strikes in north-eastern Syria last week, their associates have told the BBC.
They said they could have been hired by private military companies supporting Syrian government-backed troops.
Russia has not confirmed the deaths that were first reported by US media, saying one should not treat such reports as "primary sources".
The US says it killed more than 100 fighters in the strikes last week.
What happened in the US strikes?
The US officials say hundreds of fighters aligned with Syrian President Bashar al-Assad attacked positions of the US-backed Syrian Democratic Forces (SDF) in the Deir al-Zour province.
They crossed the Euphrates River, shelling an SDF base, where American advisers were present.
The US responded with air and artillery strikes on 7 February, thwarting the attack and forcing the pro-Assad fighters to retreat, the US officials say.
Syrian state media have reported that the strikes left dozens killed.
Meanwhile, the Russian defence ministry says that Syrian government-backed troops were hit as they launched an operation against fighters from the Islamic State group.
What about the Russian mercenaries?
Quoting a Pentagon official, CBS News first reported on 8 February that Russian mercenaries were among "pro-regime" forces that attacked the SDF base.
"If Russians are among those who were killed, this would mark the first time a US air strike has killed Russians in Syria," CBS News' David Martin reported.
More details about those killed in the strikes began to emerge in the following days.
On Tuesday, associates of two Russian fighters confirmed to the BBC that they were killed on 7 February.
The associates named the dead as Vladimir Loginov, a Cossack from Russia's western Kaliningrad region, and Kirill Ananyev, a radical nationalist from Moscow.
Some media reports suggest that dozens of Russian fighters could have been killed.
They are believed to have been employed by a private Russian company called Wagner. The firm has not commented on the reports.
How did the Kremlin react?
On Tuesday, Russian President Vladimir Putin's spokesman declined to provide any details.
"We have details of servicemen of the Russian armed forces, who are taking part in the Russian military operation in support of the Syrian army," Dmitry Peskov said.
"We don't have information about other Russians who might be in Syria.I advise you to contact the defence ministry."
And responding to a further BBC question, the spokesman said: “And, of course, you have to realise that many countries of the world have quite large numbers of our compatriots - of Russians - and, of course, it's difficult to have detailed data.”
"We recommend not treating media reports as primary sources," he added.
What are Russia's casualties in the Syrian conflict?
Moscow launched a military operation in Syria in support of President Assad on 30 September 2015.
More than 45 Russian military personnel have been officially confirmed killed since then.
An unknown number of private military contractors have also died.
Earlier this month, a Russian Sukhoi-25 ground-attack aircraft was shot down in a rebel-held area in Syria's north-western province of Idlib.
The pilot survived the initial attack and ejected, but died in a ground fight, detonating his grenade to avoid being captured.