Bilateral relations between Iraq and Syria soured in the wake of an Aug. 19 string of deadly bombings in Baghdad. Both countries pulled their respective ambassadors as Iraqi Prime Minister Nouri al-Maliki blamed Baath Party loyalists in Damascus for coordinating the attacks.
Syria denied it played a role in the plot.
Turkey, which has sought to restore the damaged relations with its neighbors, hosted Iraqi, Syrian and Arab League officials in Istanbul to help find a solution to the crisis.
Davutoglu described the process as "constructive," saying all sides recognized the importance of friendship in the region, the Voices of Iraq news agency reports.
"The meeting was positive and constructive, during which all sides underlined the importance of cooperation among countries of the region and not resorting to international forums," said Davutoglu.
Arab League Secretary-General Amre Moussa suggested both countries restore their respective ambassadors as a confidence-building measure.
Syrian Foreign Minister Walid al-Moallem relayed a message from Syrian President Bashar Assad, who said he appreciated the Turkish effort to "overcome the current fabricated crisis with Iraq," the officials Syrian Arab News Agency reports.
The ministerial meeting took place Thursday behind closed doors.