Turkey has long demanded the YPG withdraw from Syria's northern border with the nation.
On Monday, the US sought to alleviate issues at a meeting in Washington between Secretary of State Mike PompeoMichael (Mike) Richard PompeoPompeo calls for Venezuela to be suspended from OAS State Dept recognizes LGBTI Month while White House doesn't Trump says summit is on before reading "nice" letter from Kim Jong Un MORE and Turkish Foreign Minister Mevlut Cavusoglu.
"We affirm that our forces will heed the call when necessary to offer support and help to the people of Manbij should it be needed", the YPG said in a statement.
The Syrian town of Manbij, which was seized from Islamic State by mainly YPG forces, has become the epicenter of Turkish-U.S. tensions.
"Minister Çavuşoğlu and Secretary Pompeo also discussed Turkey-U.S. relations and agreed to hold further meetings of the working group mechanism to resolve current outstanding issues in the bilateral relationship".
Washington has backed the YPG, which is part of the Syrian Democratic Forces, in its fight against ISIS. Ankara calls the YPG terrorists, accusing the militia of being linked to a Kurdish insurgency inside Turkey.
"They considered the recommendations of the Turkey-US Working Group on Syria pertaining to the future of our bilateral cooperation in Syria on issues of mutual interest, to include taking steps to ensure the security and stability in Manbij".
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The US angered Turkey by announcing a plan for the formation of a Kurdish militant force in Syria near the Turkish border, prompting Ankara in January to launch a military operation against the US-backed militants.
"In the first phase, terrorist YPG will withdraw from Manbij".
United States officials confirmed the broad outline of the plan, but were keen to stress that no time-line had been fixed, that each stage of implementation would be "conditions-based" and that much work lies ahead.
The U.S. State Department did not provide further details about the agreement.
He said joint work on the US-Turkey plan, which he endorsed by his US counterpart Mike Pompeo in Washington on Monday, would begin in 10 days and be carried out within six months.
"The aim of this roadmap is the clearing of Manbij of all terror organizations and the permanent instatement of safety and stability", Cavusoglu said.
"Once [the implementation of] Manbij model is completed, a similar model will be applied to other areas of Syria occupied by the terrorist YPG", he said.