Turkey has urged the US to stop backing the Kurdish YPG in Syria, as it steps up an offensive against the militia.
A spokesman for President Recep Tayyip Erdogan told the BBC that Kurdish fighters were using US-supplied weapons against Turkish troops trying to oust them from the Afrin region.
Turkey considers the militia a terrorist group, and an extension of the Kurdistan Workers Party (PKK) which wants Kurdish autonomy within Turkey.
The YPG denies any direct links.
The militia, which controls much of north-eastern Syria, has been a key US ally in the fight against Islamic State (IS) fighters there.
The UN Security Council discussed Turkey’s growing offensive in a meeting on Monday, but did not condemn it.
Ankara is now demanding an end to the US alliance with the YPG, arguing that the fight against IS is over.
“We cannot tolerate the PKK establishing some kind of a state structure along our border in Syria,” warned presidential spokesman Ibrahim Kalin.
Thousands of civilians are reportedly trying to flee Afrin, and Syrian activists say more than 70 people have died since the Turkish push began on Saturday.
Earlier Turkish President Erdogan had vowed to “sort out” Afrin. “We will take no step back,” he said in a live television broadcast. “We spoke about this with our Russian friends; we have an agreement.”
What has happened on the ground?
On Monday, the Afrin villages of Shankal, Qorne, Bali and Adah Manli were reportedly captured, along with rural areas including Kita, Kordo and Bibno, according to Turkey’s state-run Anadolu news agency.
The YPG has denied that any of the Afrin region is under Turkish control.
It also said that it had retaliated against Turkey’s ground offensive with rocket fire on Turkish border areas. Two people died and 12 others were wounded when a rocket hit a camp housing Syrian rebel fighters near the border in Turkey’s Hatay province, local reports said.