The six troops were killed and eight others wounded in fighting with members of the outlawed Kurdistan Workers' Party (PKK) near a military base in the Cukurca district of Hakkari province.
A Kobra helicopter despatched to the scene then crashed due to a technical problem, resulting in the deaths of the two pilots, the army added.
Turkish F-16 jets, helicopters and drones were scrambled to fight the "terrorists" behind the attack and reinforcements were sent to the area.
In a separate operation in the neighbouring Sirnak province, 15 PKK members have been killed, the army said.
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Turkey has been waging an offensive against the PKK after the collapse in 2015 of a two-year ceasefire declared by the group.
Hundreds of members of the Turkish security forces have been killed in attacks since then but President Recep Tayyip Erdogan has vowed no let-up in the operations.
On Thursday night, four PKK militants said to have been loading explosives onto a stolen truck were killed in a huge explosion in an area near Diyarbakir in the southeast that was felt throughout city.
That incident came hours after at least eight people including soldiers were injured by a remotely-detonated car bomb aimed at a military vehicle in Istanbul.
There was no immediate claim of responsibility for the car bomb.
On Tuesday, three people were killed and 42 others wounded when a car bomb attack claimed by the PKK struck a police vehicle in Diyarbakir.
The PKK is listed as a terrorist group by Ankara and its Western allies but Erdogan has repeatedly accused the European Union and United States of not doing enough to halt its activities.