Western-backed rebels in Syria have said they will reject any offers of military assistance from Russia while it continues to bomb them.
Russia has said it would be willing to provide air support to "patriotic" rebels battling Islamic State (IS).
But on Monday, a Free Syrian Army (FSA) spokesman told the BBC: "They should stop attacking our bases and then we can talk about future co-operation."
Russia has insisted its air strikes in Syria are targeting only "terrorists".
However, activists have reported repeated bombings by Russian warplanes of moderate rebels and civilians in western areas where IS militants have little or no presence.
Russia began its air campaign on 30 September to bolster President Bashar al-Assad's government, after it suffered a string of defeats to both rebel forces and IS.
Despite the FSA's insistence that Mr Assad leave power, Russian Foreign Minister Sergei Lavrov said on Saturday that it was ready to support the rebel alliance in its fight against IS and to work with the US-led coalition battling the jihadist group.
"We are ready to support from the air the patriotic opposition, including the so-called Free Syrian Army,'' he said in an interview with Russian state television.
But Mr Lavrov said the US-led coalition was refusing to provide the Russian military with the locations of rebel and IS positions, calling it a "big mistake".
On Monday, a spokesman for the Southern Front of the Free Syrian Army said it would not immediately turn down the offer of air support, but expressed scepticism.
"If the Russians are serious in their offer they should stop immediately targeting our bases and targeting the civilian areas," Issam al-Reis told the BBC.
"So we didn't turn down the offer. We just said we don't need their help now."
Maj Reis added: "You know the Russians - always their words are different from their actions."
Also on Monday, Russian presidential spokesman Dmitriy Peskov dismissed as a "hoax" a report by Human Rights Watch (HRW) which said two Russian air strikes in Homs province on 15 October might have killed 59 civilians, including 33 children.
"In the last few days we have seen a huge number of media hoaxes and deliberate data releases concerning the consequences of the Russian military air campaign in Syria," he told reporters. "I think that this report is probably one of those."
HRW said on Sunday that the air strikes apparently violated the laws of war.
The Russian air campaign, along with the reported arrival of reinforcements from Lebanon's Hezbollah movement and hundreds of combat troops from Iran, has allowed government forces to launch ground offensives on several rebel-held areas.
Hosting a delegation of Russian parliamentarians in Damascus on Sunday, Mr Assad expressed his gratitude for Moscow's support and said eliminating "terrorist" groups would resolve Syria's problems.
Why is there a war in Syria?
Anti-government protests developed into a civil war that, four years on, has ground to a stalemate, with the Assad government, Islamic State, an array of Syrian rebels and Kurdish fighters all holding territory.
Who is fighting whom?
Government forces concentrated in Damascus and the centre and west of Syria are fighting the jihadists of Islamic State and al-Nusra Front, as well as less numerous so-called "moderate" rebel groups, who are strongest in the north and east. These groups are also battling each other.
What's the human cost?
More than 250,000 Syrians have been killed and a million injured. Some 11 million others have been forced from their homes, of whom four million have fled abroad - including growing numbers who are making the dangerous journey to Europe.
How has the world reacted?
Iran, Russia and Lebanon's Hezbollah movement are propping up the Alawite-led Assad government, while Turkey, Saudi Arabia and Qatar back the more moderate Sunni-dominated opposition, along with the US, UK and France. Hezbollah and Iran are believed to have troops and officers on the ground, while a Western-led coalition and Russia are carrying out air strikes.