"It must be known that the ceasefire is valid in Syria," Davutoglu said in televised remarks in the central Anatolian province of Konya.
"When it is a question of Turkey's security, then the ceasefire is not binding for us," he added.
Turkey on successive days last week targeted Kurdish fighters inside Syria with artillery barrages, saying that the army was responding to incoming fire, and had repeatedly reserved the right to open fire again.
The deal, which marks the biggest diplomatic push yet to help end the five-year conflict in Syria, excludes the Islamic State group and other Sunni extremists.
Davutoglu said Turkey would closely monitor how the ceasefire would be implemented, adding: "We support the ceasefire under any circumstances."
Turkey has demanded that the Syrian Kurdish Democratic Union Party (PYD) and its People's Protection Units (YPG) militia should remain outside the scope of the truce.
It sees both as offshoots of the outlawed Kurdistan Workers' Party (PKK), which is designated as a terrorist organisation by Ankara and its Western allies.
"There is no terror reference to YPG in the ceasefire. There should have been but there is not."
A militant Kurdish group claimed a suicide car bomb that killed 29 people in the capital Ankara last week but Turkish officials said the bomber was a Syrian Kurd working on behalf of the PYD, which has denied being behind the attack.
Davutoglu today said if Turkey's security was concerned, "we do not get permission from anyone, we do not ask anyone but we do what's required."
"When it's a question of the security measures Turkey will take, the only place to have a say is Ankara," the premier said.