Turkish soldiers stand on top of tanks in a village on the Turkish-Syrian border in Gaziantep province, Turkey.
Ankara said the U.S. had to stop backing the YPG if they wanted cooperation.
Turkish jets also hit targets at Afrin's Bursaya Mountain, which holds "strategic importance" for the Kurdish fighters, Anadolu said.
The newspaper "Hurriyet" quotes an undisclosed government source as saying that the aim of "Operation Olive Branch" is to enable self-rule for the people of Afrin so that they can build democratic institutions once the YPG has been driven out of the region.
The U.S. has urged Turkey to exercise restraint and ensure that its military offensive into Afrin is limited in scope and duration.
An emergency meeting was held by the United Nations Security Council on Monday to discuss the Turkish offensive.
They are thought to have been used by Turkey against the Islamic State (IS) group in Syria, but defence experts have speculated in German media that recent images from Turkey's "Operation Olive Branch" appeared to show them being used against Kurdish groups.
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The operation was initially presented as a exclusively Turkish offensive, with the Syrian government condemning the aggression and threatening to shoot down Turkish warplanes.
The United States hopes to leverage the YPG's control and that of US-backed Arab fighters in northern Syria to give it more diplomatic muscle as it tries to revive UN-led talks in Geneva on a deal that would end Syria's civil war.
CGTN's Michal Bardavid reports from near the Turkey-Syria border.
The US and Russian Federation have urged Turkey to show restraint in its air and ground offensive against Kurdish forces in northwest Syria. On Sunday, Syrian President Bashar al Assad called the attacks a "brutal aggression" and lamented Turkey's support for "terrorists" in Syria.
Turkey considers the YPG to be a "terrorist" group as well as the Syrian offshoot of the Kurdistan Workers' Party (PKK) which has waged a bloody three-decade insurgency against the Turkish state.
"I must take whatever step I have to". The latter has been fighting for an autonomous region inside Turkey since 1984. We spoke about this with our Russian friends.
Tillerson denied on Monday that clashes between the militia groups would hurt Turkey-US relations.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said 23 civilians had been killed in Turkish shelling and air strikes, and thousands were fleeing the fighting.