The YPG on Monday said it had agreed with Russian Federation to set up what it called a "military base" in northwestern Syria under a bilateral agreement and would help train its fighters.
One of the major forces in the Syrian conflict, the YPG is also a military ally of the United States and is playing a major part in US -backed operations against Islamic State in areas of Syria further to the east.
Redur Khalil, a spokesman for the People's Protection Units, or YPG, said the Russian forces were there "by agreement", in comments carried Monday by the group's Hawar News agency.
"This is the first agreement of its kind, although we have had previous cooperation [with the Russians] in Aleppo city", he added.
Turkey's troops pushed into Syria in August of previous year in efforts to push Islamic State of Iraq and the Levant (ISIL) away from its border and to prevent Kurdish efforts to connect its two pockets of control in Syria's north.
However, the U.S. is backing the YPG in Syria, where it considers the group a key ally in its fight against Daesh.
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Anti-ISIS forces are planning to begin an assault against Raqqa, the terrorist group's de-facto capital in Syria, with the YPG planning to fight alongside Arab forces.
The spokesman also said that the YPG aims to expand its fighting force by almost two-thirds to more than 100,000 fighters.
Moscow has staunchly denied a Reuters report claiming that it is constructing a military base in Afrin, northeast Syria, in alliance with the YPG, the Kurdish militia that controls the area. "The Russians know this, and the Americans know this and other countries know this", Kurtulmus said during a news conference in Ankara.
Josh Walker, from Bristol, fought alongside the Kurdish Militia and the YPG against Islamic extremists during a six-month stint.
Despite Moscow's massive military involvement in Syria - supporting the regime - it has been sidelined in areas of northern Syria outside Damascus' control by the US. He declined to say if the new training programme was supported by any foreign militaries.
Hemo told Reuters that the YPG aimed to "fight terrorism" everywhere in Syria, while its political priority was "guaranteeing the rights of the Kurdish people in Syria legally, constitutionally".
The hope that a nationalist rebellion would tamp down Kurdish autonomy played a big role in Turkey's early decision to back the rebels in Syria.