The Kurdish People's Protection Units (YPG) said Turkey shot at its forces in the town of Tal Abyad on Sunday.
The YPG has been a key ally of the US in fighting the so-called Islamic State (IS) group in Syria.
Turkey fears advances by the YPG near its Syrian border could fuel separatist sentiments amongst Kurds in Turkey.
The attacks come amid increasing tensions in Turkey ahead of elections.
"We said the [YPG-aligned Democratic Union Party] PYD will not go west of the Euphrates and that we would hit it the moment it did," Mr Davutoglu told Turkish ATV television late Monday.
He gave no further details.
It is not the first time the YPG has said Turkey has attacked them. In July they said Turkey had shelled them in the Kurdish-held village of Zormikhar, which Turkey denied.
In a separate incident, Turkey has confirmed detaining 30 IS militants during a dawn raid on Tuesday.
Police conducted simultaneous operations against IS cells in the central Anatolian city of Konya and the nearby town of Cumra, the Dogan news agency reported.
It comes a day after a deadly shoot-out with suspected IS militants in the city of Diyarbakir on Monday which left two police officers and seven militants dead.
Another five officers were injured and 12 militants were detained, Deputy Prime Minister Numan Kurtulmus said.
AFP news agency said this was the first clash with IS militants on Turkish soil since Turkey launched air strikes on IS targets in Syria in July.
Turkey has stepped up operations against IS since the group was blamed for twin blasts that killed more than 100 people in Ankara this month.
Tensions are running high in Turkey just five days ahead of general elections.
The double bombing in Ankara - targeting a Kurdish peace rally - was the country's most deadly, and came amid an upsurge of fighting between Turkish forces and Kurdistan Workers' Party (PKK) rebels.
Prime Minister Davutoglu said the bombings were an attempt to influence the 1 November elections.
Many of the victims were activists of the pro-Kurdish HDP party, which believes its delegation at the rally was specifically targeted.
Turkish Prime Minister Ahmet Davutoglu has confirmed that the Turkish military has attacked Kurdish fighters in northern Syria.