Lavrov made the accusations on Saturday while meeting his Turkish and Iranian counterparts in Moscow following their talks on the seven-year Syrian war, which has killed hundreds of thousands of people.
The top Iranian, Russian and Turkish diplomats said the Astana peace process is the "only global initiative that had helped practically improve the situation in Syria through joint efforts to combat terrorism, reduce the level of violence and create favorable conditions for the political settlement including via facilitating broad intra-Syrian dialogue", the statement said.
Lavrov met with Iranian Foreign Minister Mohammad Javad Zarif and Turkish Foreign Minister Mevlut Cavusoglu.
Russian Foreign Minister Sergey Lavrov and his French counterpart Jean-Yves Le Drian discussed in phone talks on Saturday the recent developments in the Syrian conflict, the Russian Foreign Ministry said.
Israel is not concerned by Russia's military presence in neighboring Syria because Moscow is a "pragmatic actor" with whom deals can be struck, Israel's Defense Minister Avigdor Lieberman said during a visit to Washington on Friday.
The final declaration of the ministers noted that the three countries would continue working on the protection of civilians and improving the humanitarian situation in Syria.
Nevertheless, he implicitly criticised Damascus after it blocked United Nations humanitarian aid to the town of Douma in eastern Ghouta, saying Moscow was calling for the regime to be more "flexible".
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Worldwide aid groups have repeatedly accused the Syrian government, which is closely allied with Russian Federation and Iran, of preventing the delivery of aid to besieged rebel-held areas.
Douma was the last town fall to a government and Russian offensive in the formerly rebel-held Eastern Ghouta region near Damascus.
Their positions on the suspected chemical attack are irreconcilable, he said.
Moscow was left embarrassed when days of warnings against the US, UK, and France were ignored and the three countries launched scores of cruise missiles on chemical weapons targets earlier this month following a toxic gas massacre in Douma, blamed on the regime.
Turkey views the Kurdish fighters as an extension of the Kurdish insurgency raging in its south east.
"Today, the U.S. supports terrorist organisations, and this has to stop", Cavusoglu said.
On Friday, regime forces seized control of buildings inside both Qadam and Hajar Al Aswad, the Observatory said.