Turkey says its warplanes bombed Kurdish militants in Iraq's Sinjar region and in northeastern Syria on April 25.
A Turkish military statement said the strikes in Sinjar were aimed to prevent the Kurdistan Workers Party (PKK) from sending weapons and explosives for attacks inside Turkey.
The PKK has been designated a terrorist group by Turkey, the United States, and the European Union.
The PKK established a presence in Sinjar after coming to the aid of the region's Yazidi population when Islamic State (IS) militants overran the area and unleashed reprisals against its Yazidi population in the summer of 2014.
A senior Kurdish military commander, General Seme Bosali, said the Turkish air strike in Sinjar killed five Kurdish Peshmerga fighters.
Turkey has regularly bombed the border area between Iraq and Turkey where PKK militants are based, but it is the first time it has targeted its affiliate in the Sinjar region.
The air strikes in Syria targeted the YPG, a key component of the Syrian Democratic Forces (SDF), which are backed by the United States and have been closing in on the IS stronghold of Raqqa.
The British-based Syrian Observatory for Human Rights said 18 YPG fighters had been killed in the strikes.
The YPG did did not immediately give its own precise death toll.
"This treacherous attack has led to the death and wounding of a number of our comrades," the YPG general command said in a statement.
It said its headquarters near Malikiya had been hit, including a media center, a local radio station, communications facilities, and military institutions.