According to BBC Turkey has launched a ground offensive in northern Syria, hours after its warplanes and artillery began hitting territory held by Kurdish-led forces.
Turkish troops and Syrian rebel allies 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.
Kurdish-led forces who were key US allies had vowed to resist.
The Kurds – who helped defeat the jihadist group Islamic State (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 those held will continue to be safely detained if ground battles break out.
In an earlier statement, Mr Trump – who had threatened to “obliterate” Turkey’s economy if it went “off limits” – said the US did not “endorse this attack”, calling the operation a “bad idea”.
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.
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.”
Turkey considers the Kurdish YPG militia – the dominant force in the Syrian Democratic Forces (SDF) – an extension of the banned Kurdistan Workers’ Party, which has fought for Kurdish autonomy in Turkey for three decades.
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.
Late on Wednesday, the land offensive began in Tal Abyad, an area under YPG control, a spokesman for one of the pro-Turkish Syrian militant groups told AFP news agency.
The Turkish government plans to send two million of the 3.6 million Syrian refugees living on its soil to the “safe zone”. The offensive could displace 300,000 people living the area, the International Rescue Committee said.
It was thought the offensive – Turkey’s third military operation in northern Syria in three years – would initially focus on a 100km (62-mile) stretch between Tal Abyad and Ras al-Ain, a sparsely populated, mainly Arab area.
But SDF spokesman Mustafa Bali said the towns of Kobane, to the west, and Qamishli, to the east, had been hit by Turkish shelling.
If Turkish troops advance towards those towns they would have to move into densely populated, mainly Kurdish areas.
Amid growing humanitarian concerns, the SDF asked the US-led coalition against IS to establish a no-fly zone to stop “attacks on innocent people”.