Members of the Democratic Union Party (PYD) on Sunday accused the Turkish military of opening fire at its forces in Tal Abyad after the majority Arab town was included into a Kurdish enclave.
In a TV interview late on Monday, Turkish Prime Minister Ahmet Davutoglu said that Turkey had warned the PYD not to cross to the "west of the Euphrates and that we would hit it the moment it did.
"We hit it twice," Davutoglu said without giving further details.
The Kurdish force has been a key ally for the US-led coalition fighting the Islamic State of Iraq and the Levant (ISIL) and controls large parts of northern Syria on the Turkish border. In June, it expelled ISIL fighters from Tal Abyad after fierce clashes.
Yet, Turkey regards the PYD as the Syrian offshoot of the outlawed Kurdistan Workers' Party (PKK) which has been fighting for more Kurdish autonomy in the southeastern areas of the country since 1984.
Last week, the Kurds in Syria said they had incorporated Tal Abyad into their "autonomous administration" in the north of the country.
The news has irked neighbouring Turkey, which fears the expansion of the influence of the Kurds, who represent about 20 percent of the country's population.
Turkey's government is concerned about a scenario in which Turkish Kurds will start cooperating with Kurds across the border in search of autonomy on both sides.
Ankara has warned Syrian Kurds to stay away from any attempts to create a "de facto situation" in Syria.
Source: Al Jazeera
