Russia is helping Syrian Kurdish YPG forces to establish a military base in northern Syria that will be used to train its fighters, the militia says.
But Russian officials have insisted there are no plans to open new bases in Syria and the one near Afrin serves as a “reconciliation centre”.
Russia says the role of the base is to negotiate local truces between the various warring sides in Syria.
Meanwhile fighting between the military and rebels has continued near Damascus.
Government forces are reportedly bombarding eastern areas of the capital, Damascus, a day after rebel fighters launched a surprise offensive.
YPG spokesman Redur Xelil told the Reuters news agency that a deal with Russia was agreed on Sunday and that an unspecified number of Russian soldiers – along with armoured vehicles – were already taking up positions at the Afrin centre.
“It is the first [agreement] of its kind,” he said in a written message.
Mr Xelil said Russian forces would help train YPG fighters on “modern warfare” and that this in turn would lead to “a direct point of contact with Russian forces”.
BBC Defence correspondent Jonathan Marcus
Russia’s move is a recognition of the Kurds’ growing importance in Syria and of Moscow’s desire to establish leverage over all of the major players in the conflict.
Russia denies that it is opening a new base but has admitted that troops have been re-located to what it calls a “reconciliation” centre in north-western Syria.
However, Kurdish spokesmen talk of the training that their forces will receive. This is likely to annoy pretty much all of the other major actors in Syria, not least the Syrian regime; but also Russia’s erstwhile new partner – Turkey; and also the Americans, who are already training Kurdish units.
It raises all sorts of questions. Might weapons supplies come with the training? And if so would they be more sophisticated than those the US has on offer, something that is certainly going to worry Ankara? And what sort of co-ordination might there be, if any, in the training effort?
Russia for its part has confirmed that it has a presence in Afrin but denies it has any military role there.
Any warming of ties between Russia and the YPG will not be welcomed by Turkey which has pledged never to allow what it terms a “terror region” to be established in northern Syria.
Opposition activists meanwhile said that heavy fighting continued in east Damascus throughout Monday with opposition-held parts of Jobar being targeted repeatedly by aircraft and artillery as fierce clashes raged along the frontlines.
Air raids were also reported in neighbouring Qaboun and Arbin.
Earlier, state media said the military had recaptured all of the territory it had lost in Sunday’s rebel assault.
Free Syrian Army factions and allied jihadist groups were involved in the attack on government-controlled Jobar and Abbasid Square, only 1.2km (0.7 miles) north-east of the Old City.
The Syrian Observatory for Human Rights, a UK-based monitoring group, said pro-government fighters and 21 rebels and jihadists were killed in the fighting.