The PM warned that Ankara would not make any concessions about the security of its borders, Censor.NET reports citing AFP.
His comments came after Russian war planes twice violated its air space in the last days.
Davutoglu said only two out of 57 bombardments had targeted IS fighters with all the others targeting moderate rebels backed by Turkey and the United States.
He said in televised remarks that the figures based on military intelligence Turkey had received.
"If there's going to be a fight against Daesh, let's do it together," he said, using the Arabic name for the group.
Davutoglu warned against any operation targeting civilians and the Syrian opposition which he said could lead to a new refugee influx.
Russian aircraft also violated Turkish airspace on Saturday and on Sunday, prompting Ankara to summon the Russian envoy to the foreign ministry twice to protest the breach.
Also, Turkish F-16 jets carrying out reconnaissance flights on the Syrian border were harassed and put on radar lock by unidentified MIG-29 planes in the last days.
"We will not make any concessions in the context of our border and air space security," Davutoglu said.
Davutoglu said Turkey's airspace was naturally NATO airspace, urging Russia to respect his country's border security while dismissing any tensions with its major trade partner.
"We do not want any tensions with Russia but as I say, it is our most natural right to expect Russia to be careful about Turkey's air space, borders and Turkey's interests in Syria," he added.
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