The statement said the military would press ahead with strikes until the rebels were "rendered ineffective".
The aircraft involved in the operation all returned safely to their bases in Turkey, it added.
Fourteen soldiers were injured in the attack by the Kurdish separatist militants in the district of Cukurca, in Hakkari province close to the Iraqi border, on Wednesday.
Officials and Turkish media said the vehicle of the troops who died was hit by a roadside bomb or mine. There were also reports of a shoot-out.
The PKK said they had carried out the attack.
Strategy questions There has been an increase in rebel attacks this summer, casting doubt on the chances of peace talks.
The latest attack will add to pressure on the government to devise a more effective strategy for combating the PKK, the BBC's Jonathan Head reports from Istanbul.
The government has already said it will ask the police to play a bigger role in counter-insurgency, he says, but this idea has been challenged by critics who argue that the police are no better equipped to tackle the PKK than the army is.
Our correspondent says there is little talk now of renewing the so-called "democratic opening", an initiative from two year ago, which aimed to end the conflict in the south-east by expanding the rights of the Kurdish minority.
The PKK, designated a terrorist organisation by Turkey, the EU and the US, has waged a 26-year insurgency against the Turkish state.
More than 40,000 people have been killed in the violence.
On Saturday, three soldiers were killed in a PKK ambush in eastern Turkey while last month 13 soldiers and seven Kurdish rebels were killed in the deadliest clash in three years.
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