Turkish forces struck Kurdish militia targets in northern Syria on February 13, and Prime Minister Ahmet Davutoglu demanded that the group withdraw from the area it recently captured.
Davutoglu said in comments shown live by state broadcaster TRT Haber that Turkey "will retaliate against every step" by the YPG militia, the armed wing the Syrian Kurdish Democratic Union Party (PYD).
"The YPG will immediately withdraw from Azaz and the surrounding area and will not go close to it again," Davutoglu said, referring to the city in the Aleppo province where nearby Turkish bombardments were reported earlier in the day.
Davutoglu did not provide precise details about the strikes. But he was quoted by the state-run Anatolia news agency as saying that they were retaliatory in nature.
"Under the framework of the rules of engagement, we responded to forces in Azaz and around that were posing a threat," Anatolia quoted him as saying during his a visit to the eastern city of Erzincan.
The news agency also quoted a Turkish military source as saying that the strikes were in line with the rules of engagement. It added that the army also responded to fire from Syrian President Bashar al-Assad's forces on a Turkish military guard post in the southern Hatay region of Turkey.
In the aftermath of the shelling, the United States urged both Ankara and the Syrian Kurds halt the violence and focus instead on tackling the "common threat" of Islamic State (IS) militants who control large parts of Syria.
U.S. State Department spokesman John Kirby said in a statement that Washington had "seen reports of artillery fire from the Turkish side of the border and urged Turkey to cease such fires."
He added that the Americans have also "urged Syrian Kurdish and other forces affiliated with the YPG not to take advantage of a confused situation by seizing new territory."
"We are concerned about the situation north of Aleppo and are working to de-escalate tensions on all sides," Kirby said.
Turkey considers the PYD and its YPG militia to be branches of the PKK, which for decades has waged an insurgency against the Turkish state.
Turkish forces have shelled YPG-controlled areas multiple times in the past.
Turkey, a member of NATO, is one of the most strident critics of Assad, whose forces have been backed by a Russian aerial campaign since September. Ankara has been a supporter of opposition forces seeking to oust Assad.
Reuters and AFP cited unidentified Kurdish sources earlier in the day as saying that Turkish forces struck the Menagh air base, near Aleppo, which was recently captured by Kurdish fighters.
Reuters cited an unidentified Turkish government source as saying that its military shelled Kurdish militia targets near Azaz, which is close to the Menagh air base.
"The Turkish Armed Forces fired shells at PYD positions in the Azaz area," Reuters quoted the source as saying.
Amer Hassan, an opposition activist based in the northern Syrian town of Azaz, confirmed to The Associated Press on February 13 that Turkish troops have shelled the based air base.
Davutoglu demanded that the Menagh base be evacuated, and he said he had spoken to U.S. Vice President Joe Biden to stress that the PYD was an extension of the PKK and a direct threat to Turkey.
His comments reflected Turkey's mounting frustration with United States backing for the PYD, which controls most of the Syrian side of the border with Turkey.