"Reinforcements were sent to the region and throughout the night support was provided to the conflict zone by attack helicopters and artillery," the army said in a statement.
"Separately, the air force struck targets identified in the northern region of Iraq."
The PKK confirmed that they had staged a deadly attack on Turkish troops.
"The military operation took place this morning in the Shemdinyan [Semdinli in Turkish] area, in Hakkari province, and Turkish warplanes have started to attack the Khwakorek district inside Iraqi territory," Ahmed Denis, a PKK spokesman, told the AFP news agency.
There has been an increase in confrontations between the PKK and the military in the mainly Kurdish southeast in recent weeks.
Turkish troops carried out on Wednesday their first ground incursion into northern Iraq in more than two years, penetrating two kilometres into the Dohuk province.
The PKK has called off a year-old unilateral ceasefire and has resumed attacks on Turkish forces.
It announced it was increasing attacks on June 1, a day after Abdullah Ocalan, the group's imprisoned chief, said in a statement that his calls for dialogue with Turkey had been ignored and that he was giving his consent to the PKK in northern Iraq to determine which course of action to take.
More than 40,000 people have been killed since the PKK launched its armed campaign against the Turkish state in 1984 in the country's southeast.