"This would simply be unacceptable... and therefore we will not allow it, of course," said Moscow's special envoy for Syria, Alexander Lavrentyev.
The withdrawal of US troops from the region, announced last week, gave Turkey a "green light", critics say.
Russia is a key military ally of Syrian leader Bashar al-Assad.
Mr Lavrentyev, during a visit to the United Arab Emirates, described Turkey's offensive as "unacceptable".
He said Turkish and Syrian officials were in contact to avoid any conflict.
And Russia's defence ministry said its forces, which have been deployed in Syria since 2015, were patrolling along the "line of contact" between Syrian and Turkish forces.
How did we get here?
The Turkish offensive, which began last week, aims to push the Kurdish-led Syrian Democratic Forces (SDF) from the border region. Turkey considers the biggest militia in the SDF a terrorist organisation.
The Turkish government wants to create a "safe zone" in the area, where it can resettle Syrian refugees currently in Turkey.
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