Turkey had been shelling the area for two days, ahead of its declaration of a military operation on Saturday.
The PKK, listed as a terrorist organization by Turkey, the European Union and the United States, has been conducting armed violence against Ankara since July 2015 after a brief reconciliation period.
Turkey has long protested the us support for the PYD - the Syrian offshoot of the terrorist PKK - and its military wing the YPG. Turkey reacted angrily to the announcement. The State Department spokeswoman Heather Nauert said on Thursday that the fight against remnants of the Islamic State, also known as ISIS, was the priority in Syria.
Moscow's green light is necessary for a Turkish operation into Afrin, where Russian military observers have deployed since past year to prevent such a confrontation.
Turkish warplanes launched air strikes on positions of the Kurdish People's Protection Units (YPG) militia in Syria, the prime minister said, as Ankara launched a new operation against the group.
Syria's Kurds have vowed to defend the land they seized in their victories over Islamic State, ... It has been unable to stop Israeli airstrikes against suspected Hezbollah targets within Syria.
Tillerson said the "entire situation has been mis-portrayed, mis-described, some people misspoke".
According to Washington's hawks, that permanent border security force would be mainly made up of Kurds, in addition to other elements. The Russian government, meanwhile, has begun troops from northern Syria.
Turkish leaders were not satisfied. Turkey was hit several times by ISIL terrorist attacks, and the YPG has been the only effective land-based military against ISIL.
"Provocative actions by the USA, aimed at isolating regions with predominantly Kurdish population, were the main factors that contributed to the development of a crisis in this part of Syria", the statement read.
Without Russian support, Turkey's intervention into Afrin would be fraught with risk, Turkish analysts said.
Differences over Syria policy have further complicated Turkey's already hard relationship with North Atlantic Treaty Organisation ally the United States. "We would call on ... the Turks to not take any actions of that sort", spokeswoman Heather Nauert reporters. The Russian military is believed to have a presence there.
This week, Erdoğan told reporters that Syrian rebels would be involved with the Turkish military's battle to take the Afrin region.
Information for this article was contributed by Matthew Pennington of The Associated Press.
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