The UN said 100,000 people had fled the violence as the number of casualties rose, while aid agencies warned nearly half a million people were at risk in north-eastern Syria.
Reflecting international fears that Turkey’s offensive could revive the so-called Islamic State group, the extremists claimed responsibility for two car bombs that exploded outside a restaurant in the Kurdish-controlled urban centre of Qamishli, killing three people.
The city was also heavily shelled by Turkish forces.
Kurdish fighters waged intense battles against advancing Turkish troops that sought to take control of two major towns along the Turkish-Syrian border, a war monitor said.
Plumes of black smoke billowed from the Syrian border town of Tal Abyad as Turkey continued bombarding the area in an offensive that was progressing “successfully as planned,” the Turkish Defence Ministry said.
Turkish troops and their allied Syrian opposition forces have advanced up to five miles into Syrian territory, Turkish vice president Fuat Oktay told TRT World television.
Turkey has said the military intends to move 19 miles into Syria and that its operation will last until all “terrorists are neutralised.”
President cleared the way for Turkey’s air and ground invasion after he pulled American troops from their positions near the border, drawing swift bipartisan criticism that he was endangering regional stability and putting at risk the lives of Kurdish allies who brought down the Islamic State group in Syria.
Defence Secretary Mark Esper said Washington is “greatly disappointed” by the offensive, which has badly damaged already frayed relations with Nato ally Turkey.
In a strong statement of support for the Kurds, Mr Esper insisted that “we are not abandoning our Kurdish partner forces, and US troops remain with them in other parts of Syria”.
Mark Milley, chairman of the Joint Chiefs of Staff, emphasised that US forces are still working with Kurdish fighters.
US troops conducted a military patrol about 19 miles south of Tal Abyad, in their first visible deployment since Turkey launched the operation.
American troops had pulled out of the border area in Syria earlier this week and Mr Trump said the estimated 1,000 US troops were not in harm’s way.
Despite the criticism, Turkish President Recep Tayyip Erdogan said his country “will not take a step back” from its offensive.
“We will never stop this step. We will not stop no matter what anyone says,” he said in a speech on Friday.
Turkey considers the Syrian Kurdish fighters to be terrorists linked to a Kurdish insurgency inside Turkey and says the offensive is a counter-terrorism operation necessary for its own national security.
The Turkish Defence Ministry said four of its soldiers have been killed since Wednesday, with three wounded. Defence minister Hulusi Akar said 342 “terrorists” — Ankara’s term for Syrian Kurdish militiamen — have been killed so far. The figure could not be independently verified.
The Kurdish-led force said 22 of its fighters were killed since Wednesday.
The Kurdish militia has fired dozens of mortars into Turkey in the past two days, including Akcakale, according to officials in two provinces on the Turkish side. They said at least 17 civilians were killed in the shelling, including a nine-month-old boy and three girls under 15.