The two-pronged operation against IS and the outlawed Kurdistan Workers Party (PKK) -- two groups who are themselves bitterly opposed -- came after a week of deadly violence in Turkey the authorities blamed on both organisations.
The strikes on the PKK threw into doubt a fragile ceasefire between Kurdish separatists and Turkey in place since 2013, with the rebels saying the conditions for observing the truce had been "eliminated".
Meanwhile Turkish ground forces pounded targets belonging to both groups with artillery from the Turkish side of the border, he added.
"No one should doubt our determination," he added. "We will not allow Turkey to be turned into a lawless country."
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Davutoglu's office said shelters and warehouses containing PKK weapons were hit in the operation in northern Iraq, where the PKK's military leadership is based.
The raids were the fiercest launched by Turkey since August 2011 when PKK targets in northern Iraq were pounded in six days of air strikes.
However Barzani's office, by contrast, said the Kurdish leader had "expressed his displeasure with the dangerous level the situation has reached," a statement from Arbil said.
The PKK has for decades waged a deadly insurgency in the southeast of Turkey for self-rule that has claimed tens of thousands of lives. A peace process that began in 2013 has so far failed to yield a final deal.
The PKK's military wing, the People's Defence Forces (HPG), denounced an "aggression of war" by Turkey and vowed "resistance".
It described the bombings in northern Iraq as the "most serious military and political error" by President Recep Tayyip Erdogan and his ruling Justice and Development Party (AKP).
The HPG statement meanwhile said that one PKK fighter in northern Iraq -- named as Onder Aslan -- had been killed in the air strikes and three others wounded.
The raids on IS and the PKK followed the killing of 32 people in a suicide bombing Monday in the Turkish town of Suruc on the Syrian border carried out by a 20-year old Turkish man linked to IS.