Rebels fired rocket launchers on an army post in Hakkari province just after midnight, NTV in Turkey said.
Military jets are pursuing them and bombing their escape routes, NTV said.
The interior minister says at least 115 rebels have been killed in a large-scale military offensive in the area in the last two weeks.
Idris Naim Sahin said the offensive close to Semdinli town - also in Hakkari province - was ongoing and that troops were taking steps to prevent rebels fleeing into northern Iraq.
The offensive is one of the biggest in years, with NTV reporting that about 2,000 troops are involved.
Several thousand Kurdistan Workers Party (PKK) rebels are believed to be based in hideouts in northern Iraq.
According to the governor for Hakkari province, Orhan Alimoglu, six soldiers, two village guards and 11 Kurdish rebels were killed in the attack near the village of Gecimili.
He said 15 soldiers were injured in the incident.
The number of clashes between the PKK and the Turkish armed forces has risen in south-east Turkey over the past year.
A series of clashes in June left dozens dead.
The PKK is classified as a terrorist organisation by the EU and the US.
It launched a guerrilla campaign in 1984 for an ethnic homeland in the Kurdish heartland in the south-east of Turkey.
It has now dropped its claim to an independent Kurdish state, but says it is fighting for autonomy and the cultural rights of the Kurdish people.
At least 19 people have died in south-east Turkey after Kurdish rebels launched an attack on a Turkish border post, according to local media.