President Recep Tayyip Erdogan of Turkey has been threatening to send troops into northeastern Syria to uproot the militia, which the United States has partnered with for years to fight the Islamic State group.
"Our mission is to prevent the creation of a terror corridor across our southern border, and to bring peace to the area", Mr Erdogan said in a tweet.
Turkey has been massing troops for days along its border with Syria and vowed it would go ahead with the military operation and not bow to the USA threat over its plans against the Kurds.
Just before Turkey launched its attack, there were reports of ISIS attacks against Kurdish forces in the northern Syrian city of Raqqa, which was previously the de facto capital of ISIS' so-called caliphate.
This is a breaking news story and will be updated.
The Kurdish-led civilian administration in northeastern Syria issued a "general mobilization" call along the Syrian border with Turkey on Wednesday as Ankara poised for an imminent invasion of the area in the latest major escalation in the war-ravaged country.
French President Emmanuel Macron is "very worried" about the planned Turkish operation, an aide told AFP on Wednesday.
He said many of these fighters are of European origin and that he had given European nations four chances to take responsibility for them.
"We have people who were displaced from Afrin because of the Turkish invasion - they are anxious that they will be displaced once again", he said, referring to Ankara's 2018 military offensive against a Kurdish enclave west of Tel Abyad.
Amid deepening humanitarian concerns, Germany said Turkey's action would lead to further instability and could strengthen ISIS, which the US-armed SDF helped defeat in Syria.
Turkish army soldiers drive towards the border with Syria near Akcakale in Sanliurfa province on October 8, 2019.
They are led by the Kurdish People's Protection Units (YPG), which Turkey considers a terrorist organization.
The Kurds say Ankara's real goal is to dilute their demographic dominance of the northeast with an influx of mostly Sunni Arab refugees from other parts of the country now living in southwestern Turkey.
Kurdish authorities in northeast Syria have declared a state of emergency and called for civilians volunteers to head to the front lines to defend against an imminent Turkish assault. Mikael Mohammed, a Kurdish father of three who owns a clothing store in Tel Abyad, a quarter-mile from the Turkish frontier, said he had not received any customers since Tuesday.
The White House said in a statement on Sunday that Turkey would now be responsible for all ISIS fighters in the area captured over the past two years.
United States troops based in the town withdrew early Monday after the White House announcement.
He responded to the criticism by threatening to "obliterate" Turkey's economy if it went "off limits" in the incursion, saying Turkey should "not do anything outside of what we would think is humane".
On Tuesday, the Pentagon said the troop withdrawal did not signal a change in the U.S. position on Syria, stressing that soldiers were moved to preserve their safety from the Turkish offensive.
"Strike them with an iron fist, make them taste the hell of your fires", the National Army, the main Turkey-backed rebel force, told its fighters in a statement.