Turkish Foreign Ministry spokesman Burak Ozugergin told CNN that Davutoglu emerged from a Monday meeting with Iraqi Prime Minister Nouri al-Maliki and was heading for Damascus.
"Our foreign minister's visit has the objective of reducing tensions between the two sides," Ozugergin told the U.S. broadcaster.
Relations between Baghdad and Damascus deteriorated after two suicide truck blasts this month in the Iraqi capital killed more than 100 people. Iraq pulled its ambassador to Damascus, saying Syria was harboring two Iraqis who allegedly perpetrated the attacks.
CNN said Syria condemned the bombings but claimed Baghdad's claims against the men were based on "fabricated evidence intended to serve internal political goals."