Turkey has launched a ground offensive in northern Syria, hours after its warplanes and artillery began hitting territory held by Kurdish-led forces.
Troops had entered the area "east of the Euphrates", Turkish officials said.
President Recep Tayyip Erdogan said the operation was to create a "safe zone" cleared of Kurdish militias which will also house Syrian refugees.
Earlier, the Kurdish-led Syrian Democratic Forces (SDF) vowed to resist any Turkish advance.
Amid growing humanitarian concerns, the SDF asked the US-led coalition against the jihadist group Islamic State (IS) to establish a no-fly zone in the area to stop "attacks on innocent people".
The Kurds - key US allies in defeating IS in Syria - guard thousands of IS fighters and their relatives in prisons and camps in areas under their control and it is unclear whether they will continue to be safely detained if ground battles break out.
The offensive was launched just days after President Donald Trump withdrew US troops from the border area, a decision that was widely condemned at home and abroad.
In a statement, Mr Trump - who had earlier threatened to "obliterate" Turkey's economy if it went "off limits" - said the US did not "endorse this attack" and had "made it clear to Turkey that this operation is a bad idea".
Asked by a reporter if he was concerned Turkish President will wipe out the Kurds, Mr Trump replied: "I will wipe out his economy if that happens."
"I've already done it once with Pastor Brunson," Mr Trump said referring to US sanctions slapped on Turkey over the detention of an American. "I hope that he will act rationally," he said.
On Twitter, Mr Erdogan said the mission "was to prevent the creation of a terror corridor across our southern border, and to bring peace to the area", vowing to "preserve Syria's territorial integrity and liberate local communities from terrorists."
Several towns and villages were hit by air strikes and artillery fire, and residents were said to be fleeing the towns of Ras al-Ain and Tal Abyad. Two civilians had been killed and two others injured in Misharrafa, west of Ras al-Ain, the SDF said.
Turkey considers the Kurdish YPG militia - the dominant force in the SDF - an extension of the banned Kurdistan Workers' Party, which has fought for Kurdish autonomy in Turkey for three decades.
The Turkish government plans to send two million of the 3.6 million Syrian refugees living in the country to the "safe zone". The offensive could displace 300,000 people living the area, the International Rescue Committee said.
It is thought the offensive - Turkey's third military operation in northern Syria in three years - will initially focus on a 100km (62-mile) stretch between Tal Abyad and Ras al-Ain, a sparsely populated, mainly Arab area.
If Turkish troops advance towards Kobane, to the west, and Qamishli, to the east, they would have to move into densely populated, mainly Kurdish areas.
SDF spokesman Mustafa Bali said both Kobane and Qamishli had been hit by Turkish shelling.
UK Foreign Secretary Dominic Raab expressed "serious concerns" about the offensive, saying it "risks destabilising the region, exacerbating humanitarian suffering, and undermining the progress made against" IS.
The UK and France planned to request an emergency meeting of the UN Security Council to discuss the situation, and European Commission President Jean-Claude Juncker urged Turkey to "halt its military operation".
Nato Secretary General Jens Stoltenberg said Turkey had "legitimate security concerns" but that he expected the country to "act with restraint and to ensure that any action... is proportionate and measured.
The EU has called upon Turkey to cease the unilateral military action
US Senator Lindsay Graham, a close ally of Mr Trump, said he would lead an effort in Congress to "make Erdogan pay a heavy price", adding: "Pray for our Kurdish allies who have been shamelessly abandoned by the Trump Administration."
According to the state news agency, Kuwait officials said the move was a direct threat to the regional stability and peace.
The UAE has condemned Turkey's actions.