The Syrian Democratic Forces, or SDF, have been a key US ally in the war on the Islamic State group and now control much of the area close to the border with Turkey.
It was Turkey's third such incursion since 2016.
On October 6, Erdogan spoke with Trump on phone, discussing the safe zone in Syria and concerns regarding YPG presence in Turkey's border.
Turkey plans to resettle 2 million Syrians in a 30 km-wide safe zone to be set up in Syria, stretching from the River Euphrates to the Iraqi border, and including Manbij.
He hosted a senior Syrian Kurdish official, Ilham Ahmed, for talks on Tuesday "to show that France stands alongside the Syrian Democratic Forces (SDF) as they are partners in the fight against Daesh (IS) and that we are very anxious by the possibility of a Turkish operation in Syria", a presidential aide told AFP.
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All of this could unravel with Turkey's military advance.
Ahead of the attack, the Syrian regime said Turkey's aggressive intentions violate global law.
He confirmed in one of his tweets that his Army is moving to the Syria, just days after the Trump administration announced it was pulling USA troops back from the border area. Cars raced to safety, although it was not clear if they were leaving the town or heading away from border areas.
The talks made no progress, but such negotiations could be an option again in the event of a wider USA withdrawal.
In Ras al-Ain, Kurdish-led security forces set up new checkpoints and stockpiled tyres to set alight to blur the vision of Turkish military pilots, an AFP correspondent reported.
"We announce three days of general mobilisation in northern and eastern Syria", it said in a statement, urging all civilians to "head to the border with Turkey.to resist during this delicate historical moment".
There has also been a chorus of global concern, including from France and Britain - the top USA partners in the anti-IS coalition - and Russian Federation, now even more firmly the main foreign player in Syria.More news: Apple’s next year iPhone models will cost more than current gen models
Turkish troops have encircled the border towns of Ras al-Ain and Tal Abyad and aid agencies fear the exodus could reach hundreds of thousands. A witness said people were fleeing en masse. If the YPG tries to hold territory there "it will lose a lot of blood", he said.
Iran's Foreign Ministry said Tuesday that the Islamic republic opposes any possible military operation by Turkey in Syria.
A spokesman for the US-backed Kurdish-led force in northern Syria said Turkish warplanes had started targeting "civilian areas" in northern Syria.
Following the beginning of the Syrian civil war in 2011, the PYD managed to take control of much of the Syria's north in the security vacuum that followed.
Minutes before Erdogan's announcement, Turkish jets began pounding suspected positions of Syrian Kurdish forces in the town of Ras al Ayn, according to Turkish media and Syrian activists.
Damascus has long viewed Turkey as an occupying power with designs on northern Syria. It has also at times suggested a willingness to strike a deal with the Kurds, though their last negotiations got nowhere.
Chaos could present Islamic State with an opportunity to stage a revival and the SDF has been conducting operations against IS sleeper cells since capturing its final territorial foothold earlier this year.
The Kurdish forces have warned of a "humanitarian catastrophe" that could potentially unfold because of the Turkish military operation.More news: Pregnant Women Should Get Flu and Whooping Cough Shots, CDC Says
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