In a new development on Wednesday, the Turkish military said it had retaliated in kind against a mortar attack from the Syrian territories under the control of the government.
The Turkish army earlier said it had conducted a strike against the Kurdistan Workers' Party (PKK) militants in an alleged bid to prevent the Kurdish forces from sending weapons to Turkey.
A statement released by Turkey's air force said that it carried out the air strikes against PKK targets located in the Sinjar Mountain region in northern Iraq, and in Karachok mountains in northeastern Syria on Tuesday.
The U.S. State Department Tuesday said it was "deeply concerned" over the strikes, which targeted the YPG - the terrorist PKK's Syrian branch - on Mt. Sinjar, northern Iraq and Mt. Karacok, northeastern Syria.
However, Kurdish Peshmerga forces in Iraq - another key USA military ally against the Islamic State - also said the Turks hit their positions, killing five of their troops.
In Washington, the State Department said it was deeply concerned by the air strikes, which were not authorized by the us -led coalition fighting Islamic State in Iraq and Syria.
The Turkish raids showed the challenges facing USA -led attempts to defeat Islamic State in Syria and risk increasing tension between North Atlantic Treaty Organisation allies Washington and Ankara over Kurdish combatants who have been crucial in driving back the jihadists.
Turkey's strikes potentially complicate the ongoing USA -led fight against the Islamic State.
Ankara has bombed the YPG in northern Syria for months, calling it a "terrorist" group because of its ties to the PKK, which has been waging a deadly insurgency against Turkey since 1984. We told them to pull their troops 20-30km south away from our borders.
"Developments in Sinjar are the result of negligence on the part of Iraq's central government, worldwide coalition forces and the us", he said.
The Kurds criticised the raids but blamed them on the PKK, saying: "These problems and tensions are all because of the PKK's presence".
Turkey's operations Tuesday were targeting the PKK, which Ankara, the United States and the European Union consider to be a terror group.
The Peshmerga in Sinjar are partly made up of Syrian Kurds, which makes for a unusual mix, because the PKK in Sinjar often receive their supplies and support often via Syria, where they enjoy warm relations with the YPG.
Vehicles that belonged to the Kurdish People's Protection Units were damaged by Turkish airstrikes in Syria.
Khalil Adar, a spokesman for the PKK in Sinjar, said none of the group's bases was targeted in the raid.
"We are fighting against [IS] with the U.S. and Turkey is hitting us from behind, giving [IS] more oxygen". "We call on the global community to intervene to put an end to these ongoing attacks on our territory", the SDF said in a statement published late Tuesday.
The YPG described Turkey's attack as "treacherous" and "barbaric" and even accused the Turks of attempting to undermine the planned offensive against Raqqa, the Syrian capital of the Islamic State.
Toner also noted that the Iraqi government had expressed concerns with Turkey's airstrikes, stressing that "military action in Iraq should respect Iraqi sovereignty".