The air force-backed operation was carried out in Yuksekova while the other six fighters were killed in fighting near the Syrian and Iraqi borders, the military said in a statement.
All the clashes occurred on Sunday, it said, according to Reuters.
After the collapse of a ceasefire between the Kurdistan Workers Party (PKK) and the government last July, Turkey's southeast has seen some of its worst fighting since the height of the Kurdish insurgency in the 1990s.
More than 40,000 people, most of them militants, have been killed since the PKK took up arms in 1984. The group wants autonomy for Turkey's Kurdish minority.