The deal with Russia followed a ceasefire agreement with the United States to pause a Turkish offensive against the Kurdish fighters, whom Ankara considers to be terrorists.
Erdogan and Putin also discussed improving bilateral ties as well as "increasing trade volume" between Turkey and Russia, Anadolu added.
Erdogan will meet US President Donald Trump on November 13 in Washington, both leaders confirmed after a phone call on Wednesday.
Turkey-backed rebels and Kurdish forces in north-eastern Syria were locked in fierce fighting on Saturday despite the ceasefire deals, the Syrian Observatory for Human Rights said earlier on Saturday.
The Turkish Defence Ministry earlier on Twitter accused "terrorists" of "carrying out a total of eight violations/attacks" over the last 24 hours, referring to the Kurdish fighters.
Turkish warplanes were separately targeting the area, the Britain-based watchdog said.
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