Two fighters were injured and then captured, they said on Thursday. The shootout, which erupted late on Wednesday in a residential neighbourhood, was part of a security operation in the city against the PKK after a policeman was killed at the weekend when PKK fighters opened fire on a police station, Anatolia news agency reported.
Unrest in Turkey's mainly Kurdish southeast has markedly escalated this year after the PKK called off a five-year unilateral ceasefire in June 2004.
On Wednesday, the group extended a truce it proclaimed last month to 3 October.
The security forces, however, have brushed this aside and clashes in the region continue.
Some 37,000 people have been killed since 1984 when the PKK, considered a terrorist organisation by Turkey as well as the European Union and the United States, took up arms for Kurdish self-rule in the southeast.