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The YPG is the main component of the US-backed Syrian Democratic Forces alliance that has seized vast territory from Islamic State in Syria.
Washington is focused on defeating IS in Syria. Ankara wants to prevent Syria's Kurds from gaining autonomy and fuelling Kurdish insurgents on its soil and last month launched a military incursion into the Afrin region of Syria to sweep the YPG from its southern border zone.
Tillerson also said the United States has had "fruitful meetings" with Europeans on the Iran nuclear deal, but said work on this issue was not yet over.