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Turkey bombarded targets in Kurdish-controlled areas on Wednesday to pave the way for an invasion Ankara says is aimed at establishing a buffer zone inside Syria.
Turkish forces attempted a ground assault on the border town of Tal Abyad on Wednesday but the Syrian Democratic Forces -- the autonomous Kurdish administration's de facto army -- said they repulsed the attack.
On Thursday, the SDF said they held off another incursion attempt in the Ras al-Ain area, further east.
Our forces "confronted a field incursion attempt by the Turkish occupation army on the axis of Tal Halaf and Aluk," the SDF said in a statement.
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The Turkish defence ministry insisted the operation was going as planned.
"The Peace Spring Operation was successfully conducted overnight, from the air and on the ground," it said in a statement.
"The designated targets were captured," it added, without specifying what they were.
Turkish media reports suggest the main goal of the operation is to create what Ankara calls a "safe zone" over an area about 30 kilometres (20 miles) deep and stretching about 120 kilometres along the border between Ras al-Ain and Tal Abyad.
Turkey's troops and Syrian proxies have yet to enter either of the two towns but are moving into surrounding villages and countryside.
The area is less densely populated than other Kurdish-controlled areas and mainly Arab.
AFP correspondents on the Turkish side of the border said Thursday that dozens of vehicles carrying Syrian former rebels fighting for Ankara crossed into Syria.
They were cheered by Turkish well-wishers as they passed the crossing in Akcakale.
The massively outgunned SDF are expected to focus their defence on the area's main towns and have called up civilians to join the resistance against the Turkish assault.
According to the Syrian Observatory for Human Rights, at least 19 members of the SDF and eight civilians have been killed by Turkish shelling and air strikes so far.