SDF commander met with Russian generals - including Major General Alexander Chaiko - at an undisclosed location in Syria on Tuesday, according to the
Kurdistan24 news site.
Abdi said that the talks centred on an alleged drone strike that killed three Kurdish activists near the Syrian city of Kobani on 23 June.
The SDF said this violated a "safe zone" agreement agreed between Moscow and Ankara in October.
"We received today the of Commander of the Russian forces in Syria, Major General Alexander Chaiko to discuss common issues among them the violations of Turkey of the 23rd October agreement, in particular the assassination of three Kurdish female activists in Kobani," General Abdi tweeted.
"It has been agreed to raise the level of coordination and joint work. And we have directed thanks to his responsiveness in working to confront the challenges."
Turkey has launched three major offensives into northern Syria, targeting the Islamic State group and Kurdish People's Protection Units (YPG), which Ankara considers part of the "terrorist" Kurdistan Workers' Party (PKK).
Social media has been rife with rumours about a new Turkish operation against Kurdish militias in northern Syria.
Turkish President Recep Tayyip Erdogan held talks with Iran President Hassan Rouhani and Russian President Vladimir Putin last week on the issue of Syria.
Days later there were rumours that Russian forces flag at the Ain Al-Issa base in SDF territories had lowered their flag, sparking concerns that the troops were withdrawing from the area, paving way for regime or Turkish attacks, according to
Kurdistan24.
Russia has pushed for the SDF to cede some of its territories to Bashar Al-Assad's regime, when Turkey launched its last major offensive in northern Syria last October.
Russian media reported a visit by Syrian special forces commander Suhail Al-Hassan to and that regime reinforcements were being sent to the area.
"Suheil Al-Hassan toured several military points in the region, and met with a number of regime officers," a source told Russian media, according to
Baladi News.
"Huge Syrian military reinforcements have recently arrived in the Raqqa countryside, loaded with ammunition, before being spread out in the region."
The reports hinted at a possible new offensive being planned by the Syrian regime on SDF-controlled areas in northeast Syria.
Syrian regime forces moved into some SDF-controlled territories when Turkey-launched military operations last year.
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