The main Turkish efforts were focused on the towns of Ras al-Ayn and Tell Abyad. Turkey-led forces captured several villages surrounding the towns and event entered Tell Abyad.
Turkish and allied forces faced stiff Kurdish resistance on Friday as they battled to seize key Syrian border towns, on the third day of a broad offensive that has sparked a civilian exodus.
President Donald Trump, whose order to pull back US troops from the border this week effectively triggered the invasion, said Washington would now seek to broker a truce.
The third such Turkish operation since the start of the war in Syria, was met with fierce international condemnation, including among Trump’s own allies, over what many saw as the blatant betrayal of a faithful ally.
The Kurdish-led Syrian Democratic Forces were fending for themselves, trying to repulse multiple ground attacks along a roughly 120 kilometer (75 mile) long segment of the border.
“There is heavy fighting between the SDF and the Turks on different fronts, mostly from Tal Abyad to Ras al-Ain,” the Syrian Observatory for Human Rights said.
The Britain-based war monitor said the Turkish forces and their Syrian proxies — mostly Sunni Arab ex-rebels — were deploying air strikes, heavy artillery and rocket fire.
“The SDF are using tunnels, trenches and berms” in their defense operations, the Observatory said.
The monitor said four civilians were killed in Tal Abyad when an air strike hit the car in which they were fleeing the fighting, while another three were shot dead by snipers around the border town.
That brings the civilian death toll to 17 on the Syrian side, while seven have also been killed in Turkey.
According to the Observatory, 41 SDF fighters have also been killed while Turkey has reported the death of only one soldier.
Kurdish counter-attacks overnight led to the retaking of two of the 11 villages they had lost since the start of the Turkish-led assault on Wednesday.
The Observatory and a Kurdish military source said several Arab families in the border area had sided with Turkey, raising sleeper cells to attack from behind SDF lines.
An AFP correspondent in the Ras al-Ain area said new units of Syrian former rebels were being brought in to break Kurdish resistance.
Ras al-Ain, Tal Abyad and other border towns between them have been almost emptied of their population in a huge wave of displacement.
Most of the 70,000 people the United Nations confirmed had been displaced traveled east towards the city of Hasakeh, which has not been targeted by Turkey.
On Twitter on Thursday, Trump said that he hoped to “mediate a deal between Turkey and the Kurds” — saying the alternatives were sending in “thousands of troops” or hitting Turkey hard with sanctions.
A US official explained that Trump had asked diplomats to try to broker a ceasefire and argued sanctions against Turkey were not justified at this stage.
Doctors Without Borders (MSF) said in a statement that it had to close down the hospital it supported in Tal Abyad.
The shelling there led most people to leave, including the hospital’s medical staff, it said.
Turkey is still far from having reached the goals of its military invasion but the risk appears to be growing that detained IS fighters could break free.
Russian President Vladimir Putin said he doubted Turkey would be able to ensure IS prisoners stay behind bars.
According to the Kurdish administration, some 12,000 men are held in seven detention centres across Kurdish-controlled areas.