"We are deeply concerned at what is happening in the Syrian-Turkish border area," the ministry said in a statement.
Turkey's air and ground operation risks "further degeneration of the situation in the conflict zone," Moscow warned.
The Turkish offensive targeting both Islamic State extremists and Syrian Kurdish militias could lead to deaths among peaceful civilians and "flare-ups of inter-ethnic tensions between Kurds and Arabs," it added.
Russia, a major ally of the Syrian regime, has strengthened its relationship with Syria's Kurds and a Kurdish representative office recently opened in Moscow.
It called for "broad intra-Syrian dialogue with the participation of all the ethnic groups and confessions including Kurds."
Ankara has always called for the ouster of Assad as the key to ending the conflict, putting Turkey at odds with both Russia and Iran.
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