The move also prompted US soldiers to withdraw from a nearby base.
A US military official said the situation across Rojava was “deteriorating rapidly” and that American forces were cut off from the Syrian Kurdish fighters they had previously partnered with.
The official said US troops on the ground are at risk of being “isolated” and cannot travel overland without a “high risk” of armed confrontation with Turkey-backed forces.
The camp in Ein Eissa, around 20 miles south of the border, is home to some 12,000 people, including 1,000 wives and widows of Daesh fighters and their children.
The Kurdish-led administration in Rojava said in a statement that 950 Daesh supporters escaped after attacking guards and storming the gates.
The UK-based Syrian Observatory for Human Rights (SOHR) said Turkish warplanes struck villages near the camp on 13 October.
It said camp residents fled as Turkey-backed Syrian fighters attacked Kurdish forces, without providing an exact number.
Jelal Ayaf, a senior official at the camp, told local media that 859 people successfully escaped from the section housing foreigners.
He said a few were recaptured but that supporters inside the other section of the camp also escaped and were carrying out attacks. He described the situation as “very volatile”.
The US official said a “small group” of American troops withdrew from a base in the town because of the threat posed by Syrian fighters allied with Turkey, but that US forces were still present in larger bases nearby.
The Kurdish-led Syrian Democratic Forces (SDF) were a key US ally in the war against Daesh and drove the extremists from most of the territory they once held in northeastern Syria.
The force swept up thousands of Daesh fighters and their family members in the campaign and has warned it may not be able to maintain its various detention centres as it struggles to repel the Turkish advance.
The progressive Kurdish-led YPG and YPJ militias are at the heart of the SDF. These forces defeated Daesh in its de facto Syrian capital of Raqqa. Yet Turkey classifies these groups as terrorist organisations, with no valid justification.
It launched the operation earlier this week after Donald Trump moved US forces aside, saying he was committed to getting out of America’s “endless” wars.
Turkish presidenton Sunday ruled out any mediation between Ankara and what he calls a “terror group”.
The United Nations says more than 130,000 Syrians have fled since the operation began five days ago, including many who had taken refuge from previous rounds of fighting in the country’s eight-year civil war.
Turkey’s defence ministry tweeted on Sunday that its forces had invaded the main road running between Hassakeh, a major town and logistics hub, and Ein Eissa, the administrative centre of the Kurdish-held areas.
Heavy fighting was also underway in the town of Suluk, north-east of Ein Eissa.
Turkey’s official news agency said Syrian fighters allied with Ankara had captured the town, while Kurdish officials said they were still battling to hold onto it.
The Anadolu news agency said Turkey-backed forces had cleared the town centre of Suluk, which is located at a strategic crossroads about six miles south of the border.
Smoke could be seen rising from several points in the Syrian town of Tel Abyad, near the border, as a machine-gun mounted pick-up truck filled with Turkey-backed Syrian fighters drove along the outskirts. In the distance, a flag of the main Kurdish militia could still be seen waving from a tall post.
Turkish troops and their Syrian allies have made already captured several northern villages in fighting and bombardment that has killed and wounded dozens of people.
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