The military said there were also "several" injured members of the "separatist terrorist organisation" -- Turkey's official term for the outlawed Kurdistan Workers' Party (PKK) -- after the strikes in the Asos region on Monday.
It was not possible to independently verify the toll.
The strikes also damaged a PKK shelter, tunnel and hideout, the armed forces said, adding it destroyed a large ammunition store and two armoured vehicles.
The PKK has waged an insurgency inside Turkey since 1984 and is blacklisted as a terrorist organisation by Turkey, the United States and the European Union.
Following the collapse of a two-year ceasefire in 2015, Turkish military operations against the PKK intensified in southeastern Turkey.
Turkey also regularly conducts air raids against PKK militants who have rear bases in the Qandil mountain area of Iraq, while Turkish ground troops sometimes stage incursions into the area.
Last month four Turkish soldiers were killed in northern Iraq in two separate attacks blamed on the PKK.
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