However, a US embassy official, asked to comment on Buyukanit's remarks, told Reuters news agency: "We have not approved any decision. It is not for us to approve. However, we were informed before the event."
Iraqi officials said 10 villages were bombed early on Sunday morning, leaving at least one woman dead and forcing hundreds of people to flee.
Abdullah Ibrahim, mayor of Sankasar town, said that 200 families had fled their homes in villages in the Sankasar and Jarawa administrative areas and at least 10 houses had been destroyed.
Iraq's deputy foreign minister, Mohamad Hmoud, summoned the Turkish ambassador and demanded an end to the air strikes, which "may affect the friendly relations existing between the two peoples and governments", the foreign ministry said.
The foreign ministry also said a clinic and a school had been destroyed, and bridges ruined.
Ankara denied that civilian areas had been hit in the attacks.
"Warplanes of the Turkish air force conducted a comprehensive air campaign against targets belonging to the terrorist PKK-Kongra Gel organisation in the Qandil mountains from 0100 this morning," a Turkish military statement said.
"The operations solely target the ... terrorist movement. They are not conducted against people living in northern Iraq or local groups not engaged in enemy activity."
Turkish ground forces have also been shelling the area where fighters belonging to the outlawed Kurdistan Workers Party (PKK) are believed to be operating, the statement said.
Buyukanit said that Sunday's attacks had been successful and all targets destroyed.
"No civilian targets or villages were hit even accidentally," he said.
"The Turkish armed forces have given the message to the Turkish public and the world that whether it is winter or summer, we will find and hit them even if they live in caves."
Thousands of troops
Ankara has massed up to 100,000 troops, backed by tanks, artillery and military aircraft, along the mountainous border.
The Iraqi foreign ministry said that the Turkish military activity "may affect the friendly relations between the two governments and peoples".
"This attack has destroyed hospitals, schools and bridges. We demand that Turkish authorities stop such actions against innocents," Mahmoud al-Hajj Humoud, deputy foreign minister, said in a statement.
But Recep Tayyip Erdogan, Turkey's prime minister, has warned that his government was determined to use every kind of instrument in the fight against the PKK.
"We will continue to wage this battle for our nation's unity and peace, both inside and outside Turkey," he said in televised comments made during a visit to the Aegean port of Izmir.
Turkey claims the right of self-defence under international law to stage cross-border attacks against an estimated 3,000 PKK fighters in northern Iraq.
Ankara blames the PKK, which seeks a separate Kurdish homeland in southeastern Turkey, for the deaths of nearly 40,000 people since it began its armed struggle in 1984.
Despite Sunday's actions, a major incursion is not seen as imminent.
Many Kurdish fighters are believed to have moved into neighbouring Iran and weather conditions in northern Iraq are worsening, making a large-scale military strike difficult.