Russia says its airstrikes are against the Islamic State group (IS), and have so far hit five targets belonging to the jihadists, but Washington has disputed this and argues they are in fact aimed at supporting Syrian President Bashar al-Assad.
The Pentagon held what they said were "cordial and professional" talks with Russian officials on Thursday in a bid to avoid mishaps between the two military powers in the region.
A US-led coalition has been targeting IS for about a year and is carrying out near-daily airstrikes in Syria, but the Pentagon worries any run-in with Russian planes could spark a major international incident.
Tensions have been running high at the UN where Russia and Iran, both support Assad, have clashed with Western powers that argue removing him from power is vital to end Syria's bloody four-year civil war.
IS has taken advantage of the chaos to seize territory across Syria and Iraq, which it rules under its own brutal interpretation of Islamic law, and has recruited thousands of foreign jihadists to its cause.
Speaking ahead of his talks with Putin, Hollande said airstrikes in Syria should target IS exclusively.
He said it was essential to ensure that "the strikes, regardless of who is carrying them out, target Daesh and not other groups", using the Arabic acronym for the Islamist group.
Foreign Minister Sergei Lavrov told the UN Russia was targeting the same terror groups as the US-led coalition, including IS and Al-Qaeda's Syrian affiliate the Al-Nusra Front.
"If it acts like a terrorist, if it walks like a terrorist, if it fights like a terrorist, it's a terrorist, right?" he asked.
Putin also rejected allegations that civilians had been killed in Russian raids, dubbing the reports "information warfare".
Russia's defence ministry said it had hit five IS targets, including a training camp and command post in northwest Idlib province.
"We have prevented IS fighters from re-establishing a command post in... Hama province that had been destroyed," added Russian defence ministry spokesman Igor Konashenkov.
Earlier Moscow said its raids had destroyed a "terrorist" headquarters, a weapons warehouse, a command centre and a car bomb factory.
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