The Russian Foreign Ministry said on December 12 that Lavrov and Jaafari had spoken by phone to discuss the "unlawful incursion," RFE/RL has reported.
"The Russian side expressed its firm position in support of the sovereignty and territorial integrity of Iraq," the statement said.
Meanwhile, thousands of Iraqis have taken to the streets of Baghdad and Basra to protest against Turkey's deployment of troops in the north of the country.
"We consider any military presence on Iraqi land as foreign aggression which we should stand against using all possible means," Hadi al-Amiri, a Shi'ite lawmaker who heads the armed Badr Organization, told protesters gathered in central Baghdad's Tahrir Square on December 12.
Many participants were members of Shi'ite paramilitary forces who held up banners reading "Death to Turkey."
A similar rally was held in the southern city of Basra.
News of the deployment of Turkish soldiers to a base near Mosul last week has triggered a crisis between Ankara and Baghdad, which demands their immediate withdrawal.
Turkey refuses, saying the troops were deployed to protect trainers working with Kurdish Peshmerga forces fighting the Islamic State group.
