The YPG is designated by Ankara as a terrorist group and an extension of the Kurdistan Workers Party (PKK), which has waged a three-decade insurgency on Turkish soil in which more than 40,000 people have been killed.
Russian President Vladimir Putin and his Turkish counterpart Recep Tayyip Erdogan made the remarks during a telephone conversation, according to a Kremlin statement, Xinhua reported.
The Turkish military said two soldiers were killed when their attack helicopter crashed and was destroyed.
The United States had until now backed the Kurdish militias with military intelligence, air-strike assistance, weapons, and training in their fight against the jihadist group.More news: Adam Schiff: Republicans' Hypocrisy on FISA Memos 'Grabs You By the Throat'
As Turkish Armed Forces continued to deploy military vehicles at the border close to the operation area, smoke was seen rising from various fields in Syria.
Two senior U.S. generals have visited Manbij on Wednesday with outsized U.S. flags on their vehicles, and one of them said "You hit us, we'll respond aggressively", in response to Turkish threats, according to U.S. reports, clearly a sign of mounting tensions on the war terrain.
At least 17 Turkish military personnel have been killed in the three-week offensive to clear Afrin of the Kurdish YPG militia.
The clash marked a fresh escalation between Washington, which has threatened the regime over its alleged use of chemical weapons, and Damascus, which labelled the latest incident in eastern Syria a "war crime".
UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein says the past week "has been one of the bloodiest periods of the entire conflict".More news: These Olympic Athletes Are Using Tinder At The Winter Olympics
Both Idlib and eastern Ghouta are part of Russia-negotiated de-escalation areas, which are meant to freeze the lines of conflict and allow in humanitarian aid.
The dramatically increased number of airstrikes and ground-based strikes on the besieged Rural Damascus area of Eastern Ghouta, where some 350,000 people are believed to remain trapped, have killed at least 210 civilians - over a quarter of them children and 42 of them women - mostly between 5 and 8 February. At least two million people live in Idlib, the largest area controlled by the opposition.
Calling for "urgent worldwide action" to protect civilians, Zeid also slammed what he called an "epic failure of global diplomacy" to end the seven-year-old war.
"They reaffirmed mutual commitment to the political and diplomatic resolution of the crisis based on UN Security Council Resolution 2254, in line with the decisions of the Syrian National Dialogue Congress, which was held on January 30, 2018 in Sochi", the Kremlin said.More news: Huddersfield boss Wagner delighted with 'huge win' over Bournemouth
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