A small number of people were injured in the incident in the town of Iskenderun, in Hatay province, the region's governor said, adding that none of them were in serious condition.
Gov. Rahmi Dogan said police tried to stop the militants' vehicle at a road block close to the nearby town of Payas, triggering the police chase that continued into Iskenderun.
The suspects then tried to escape on foot. One of them died after setting off an explosion, while the second was killed by the security forces, Dogan told reporters. CNN-Turk television said the explosion was caused by a hand grenade.
Dogan added that the two suspects were part of a group of four militants who had flown to the Amanos from the Syrian town of Manbij, in Aleppo province, using powered paragliders. He did not identify the suspects.
The PKK has led a decades-long insurgency in Turkey’s mainly Kurdish southeast region and is considered a terrorist organization by Turkey, the United States and the European Union. The conflict has led to the loss of tens of thousands of lives since it started in 1984.
The explosion caused significant damage to cars and shops, the state-run Anadolu Agency reported. Earlier, it said police, fire service rescuers and medical teams were dispatched to the area.
The incident came days after the U.S. Embassy in Turkey issued a security alert, saying it had received reports of a possible attack on Americans and other foreigners and urging U.S. citizens to exercise caution.
The PKK and the Islamic State extremist group conducted deadly attacks on Turkish soil between 2015 and 2017.