The Turkish military operation, launched Wednesday, followed a U.S. decision to pull troops from a strip of northern Syria controlled by Syrian Kurd-led militias who led the fight against the Islamic State.

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Neighboring Turkey views the largely Kurdish-controlled force as a terrorist group on its doorstep and a threat to its national security. But the multiethnic force, known as the Syrian Democratic Forces, or SDF, had worked alongside U.S. troops for years, suffering 12,000 combat casualties as they pushed Islamic State militants from towns and cities, taking and holding territory in the process.

Turkish forces advanced on the key border town of Ras al-Ayn on Saturday, trying to seal a first major advance in the campaign to carve out a Turkish-controlled zone. With hold of the town comes access to a major arterial road.

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Turkey’s Defense Ministry said Ras al-Ayn had been “brought under control” following clashes with the SDF. The Kurdish-led force denied that troops had seized the town.

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“Ras al-Ayn is resisting, and clashes are continuing,” said Mervan Qamishlo, an SDF spokesman.

Dozens of Syrian and Turkish civilians have been killed in the fighting. Mortar fire from Kurdish fighters has emptied Turkish border towns. A much heavier bombardment by the Turkish military has civilians streaming away for safer ground.

More than 100,000 people have fled along an 80-mile strip between Ras al-Ayn and Tel Abyad, to the west, in recent days, according to the United Nations.

Reached by phone, displaced civilians in Syria described an atmosphere of rising dread as the violence worsened and families camped out wherever they could find space.

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“The sound of fighter jets is scaring the children; even the adults who are supposed to calm them down can’t hide their fear,” said Nowruz, a woman from a village near Ras al-Ayn, who spoke on the condition that only her first name be used because of worry for her family’s security. “What people have been fearing for years [has] come true. We didn’t know what to do.”

In the city of Hasakah, about 50 miles southeast of Ras al-Ayn, Kurdish writer Nariman Evidke said she had fled Ras al-Ayn with nine members of her extended family. But one was missing: an uncle who was a fighter. He disappeared as mortars rained down around the town days earlier.

In daylight hours, she said she had combed the city’s hospitals and morgues, without success. At night, she huddled with her family and made what calls she could as cellphone networks faltered.

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“I cannot describe what I have seen,” she said, voice shaking. “In the morgue, we saw a young man’s body with a severed leg on the bed next to him. In the hospital, there was an old man, wounded and just lost. He seemed to have no family.”

Turkey has said it intends to press 18 miles into Syrian territory — a goal that seems increasingly difficult as international alarm about the offensive escalates.

Virtually all of Turkey’s major allies have expressed fears that the Islamic State will reemerge as a result of the operation, as the Kurdish fighters are called away to the Turkish front. Those worries were brought into sharp relief Friday, when the SDF said five Islamic State detainees had escaped from a prison in eastern Syria.

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The SDF forces control jails housing thousands of alleged Islamic State fighters, as well as several displacement camps where tens of thousands of civilians — some of them families of the militants — are penned in amid worsening conditions and rising anger.

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American forces are still stationed farther south in Syria’s Kurdish-dominated region, and the U.S.-led coalition says it is continuing counterterrorism operations against the Islamic State. But U.S. and Kurdish officials already acknowledge in private that the violence has hampered that fight at a critical time.

Trapped in the middle, civilians interviewed by phone in the Syrian border zone said they felt betrayed by a U.S. pullout that now left them vulnerable to Turkish bombs and Islamic State attacks. They worry that sleeper cells are dotted across the region. On Friday, attackers proclaiming allegiance to the Islamic State claimed responsibility for a car bomb outside a usually packed restaurant in the Syrian city Qamishli. Reports on casualties were unclear.

“If they do not want to protect us, what are they doing here?” asked Nowruz, referring to U.S. forces. “Why are they still in Syria?”

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Turkey views Syria’s Kurdish fighters as terrorists for their links to the Kurdistan Workers’ Party, or PKK, which has waged a decades-long battle for greater autonomy in Turkey.

Using warplanes and an allied Syrian ground force, President Recep Tayyip Erdogan’s offensive is advancing into Syria along roughly 80 miles of the shared border, between the Syrian towns of Tal Abyad in the west and Ras al-Ayn in the east, Gen. Mark A. Milley, the Pentagon’s top general, said in a media briefing Friday.

The flat landscape in that zone favors Turkey’s conventional military in the battle, analysts said.

But for days, the Syrian Kurds have been able to carry out deadly strikes across the border — into Akcakale, across the border from Tal Abyad, and into Ceylanpinar, the Turkish town that borders Ras al-Ayn. Firefights have terrorized neighboring towns farther east as well, including Qamishli, in Syria, and the Turkish town of Nusaybin, half a mile away.

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Doctors Without Borders, the medical charity, said a hospital it supported in Tal Abyad — the only public hospital in the immediate region — closed after the medical staff fled the town, along with their families. Kurdish authorities said another hospital, in Ras al-Ayn, was temporarily closed after it was struck by Turkish shelling.

As civilians moved to what safety they could find, reports Saturday suggested a buildup of hundreds along a border crossing into Iraq’s Kurdish region. Aid groups have scrambled to receive them: A camp has been prepared, and reception centers are ready at the border crossings.

“It is crucial that all actors ensure civilians can safely and voluntarily escape the violence in [northeast] Syria and seek protection in Iraq,” said Tom Peyre-Costa, a spokesman for the Norwegian Refugee Council. International funding to support any influx would be critical, Peyre-Costa said.

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“We fear a spillover into Iraq could spark instability,” he said.