Turkey launched an assault on Kurdish forces in northern Syria on Wednesday with air strikes and artillery fire reported along the border.
President Recep Tayyip Erdogan announced the start of the attack on Twitter, labelling it "Operation Peace Spring".
It triggered criticism from Western countries who have allied with the Kurdish-led Syrian Democratic Forces (SDF) against the Islamic State jihadist group (IS).
An AFP correspondent reported Turkish artillery fire in the Ras al-Ain border area and explosions as warplanes flew overhead.
Kurdish forces said at least two civilians were killed.
SDF fighters armed with rocket launchers were seen deploying in the area, as Kurdish authorities called up civilians to defend against the assault.
The Syrian Observatory for Human Rights war monitor said air strikes and artillery fire also hit the Tal Abyad border region further west.
The SDF called on the international community to impose a no-fly zone to protect against "an imminent humanitarian crisis".
Erdogan said the operation would target both Kurdish militants and IS.
"Our mission is to prevent the creation of a terror corridor across our southern border, and to bring peace to the area," he wrote on Twitter.
Ankara says it is necessary to curb the power of the SDF due to its ties with Kurdish insurgents inside Turkey.
It also wants a "safe zone" on the Syrian side of the border where it could send back some of the 3.6 million refugees it hosts from the eight-year civil war.
President Donald Trump insisted the United States had not abandoned its Kurdish allies.
Trump was widely seen as giving a green light at the weekend, ordering the pullback of US troops from the Turkey-Syrian border which had served as a buffer.
Russian President Vladimir Putin urged Erdogan to "think carefully" before the offensive, while the European Union demanded Turkey halt its military operation.
Kurdish authorities announced a general mobilisation, urging all civilians to "head to the border with Turkey... to resist during this delicate historical moment".
Shortly after fighting started, Anadolu news agency said two shells hit the Turkish town of Ceynalipinar and six rockets hit Nusaybin.
"Both Turkish and Kurdish forces have a track record of carrying out indiscriminate attacks in Syria that have killed scores of civilians," warned Amnesty International's Middle East research director Lynn Maalouf.
"This must not be allowed to happen again," she added.
Kurdish leaders said they would hold their erstwhile US ally and the whole international community responsible for any "humanitarian catastrophe".
In Ras al-Ain, Kurdish-led security forces set up checkpoints and stockpiled tyres to set alight to blur the vision of Turkish military pilots, an AFP correspondent reported.
Ras al-Ain was one of the places from which US troops withdrew on Monday.
"We will not leave this land," said Kawa Sleem, a 32-year-old Ras al-Ain resident.
"War has been chasing us for years, and everyday Erdogan threatens us with a new attack," he added.
It was expected that Ras al-Ain and Tal Abyad -- both with Arab-majority populations -- would be the focus of the first assaults.
Kurdish forces have dug trenches and tunnels in both areas, covering streets with metal canopies to block the cameras of Turkish drones.
The Kurdish-led SDF took heavy losses in the US-backed campaign against IS in Syria which they led to its successful conclusion in March.
Trump has faced a barrage of criticism, including from close allies in Washington, for appearing to leave US allies to their fate.
Senior Republican senator Lindsey Graham addressed a tweet to the Turkish government saying, "You do NOT have a green light to enter into northern Syria.
"There is massive bipartisan opposition in Congress, which you should see as a red line you should not cross."
There has also been a chorus of international concern, including from US allies.
Russian Foreign Minister Sergei Lavrov said that Iraqi Kurdish leaders he met earlier this week had voiced deep concern about the mixed signals from Trump.
"They are extremely alarmed that such a lightweight treatment of this extremely delicate subject could ignite the entire region," Lavrov said.
Since 2015, Russia has been the main military backer of the Syrian government, which has seized on the policy shift from Trump to try to persuade the Kurds to accept the restoration of central government control.
The Kurds called on Moscow on Wednesday to facilitate dialogue with Damascus.
They have warned that a Turkish offensive would reverse the military gains achieved against IS and allow the jihadist group's surviving leaders to come out of hiding.
While a Kurdish-led operation earlier this year saw the end of IS's territorial caliphate, the organisation is not dead and sleeper cells have been active in several parts of Syria and Iraq.
IS claimed an overnight suicide attack by two of its fighters in its former Syria stronghold of Raqa.
Turkey said it would not allow a resurgence of IS, but called on European countries to repatriate jihadist prisoners being held in Kurdish detention centres.