His comments came after Syria's Democratic Union Party captured the border town of Ras al-Ain, Today's Zaman reported.
The capture of the town has fueled Turkish officials' fears that an autonomous Kurdish state will be created that would fortify homegrown terrorists. Davutoglu warned against that possible development Friday and said it would lead to more clashes in the country.
Turkey beefed up its military presence on the Syrian border Friday, and warplanes flew low over the area, the Hurriyet Daily News said.
Authorities said the planes didn't violate Syrian airspace and were inspecting the area for the safety of Turks.
Soldiers and tanks were also dispatched to the border.
Turkish troops fired shots at Democratic Union party fighters in Syria after two rocket-propelled grenades struck a border post in Turkey, Today's Zaman said.