BEIRUT - Swift Turkish advances deep into Syrian territory on Sunday triggered a panicked exodus from a strategic Syrian town - and the unraveling of the U.S. mission in northeastern Syria.

Hundreds of Islamic State family members are believed to have escaped a detention camp in the town of Ain Issa, 20 miles from the Turkish border, as Turkish shellfire hit the area. U.S. troops pulled out from their base in the town, as Turkish-backed Syrian rebels consolidated their hold over a vital highway nearby, cutting the main U.S. supply route into Syria and isolating troops based further west.

By the time Defense Secretary Mark Esper appeared on CBS' "Face the Nation" to announce that President Donald Trump had ordered the final withdrawal of the 1,000 U.S. troops in northeastern Syria, U.S. officials said, it was already clear that the U.S. presence had become unsustainable.

The withdrawal of a small number of U.S. troops based in Ain Issa was followed by reports from aid workers and the U.S. allied Syrian Democratic Forces that hundreds of Islamic State supporters appeared to have escaped from a camp for displaced people, having taken advantage of the mayhem as Turkish artillery pounded the area and civilians also fled.

The Kurdish administration in northeastern Syria said 785 people affiliated with the Islamic State escaped from a camp that had housed 12,000 displaced people, mostly women and children.

Around a thousand of those, almost all foreigners, had been identified as Islamic State supporters, and were housed in a separate section of the camp known as the Annex. That section is now "completely empty," according to an aid worker who spoke on the condition of anonymity because they were not authorized to talk to the press.

The claim that the Islamic State-linked families had escaped could not be independently confirmed, but Kurdish officials and aid groups said thousands of civilians were also leaving, fleeing across fields to escape the shelling. Aid workers were told to evacuate by the U.S. military.

Ain Issa, which served as the headquarters of the Kurdish-led administration in northeastern Syria, owes its significance to its position beside the important M4 highway, which runs across northeastern Syria from the Iraqi border. It's the main supply route in and out of Syria for the 1,000 U.S. troops deployed there, as well as for much of the limited aid that reaches northeastern Syria.

As the Turkish-backed Syrian rebels closed in Sunday, the small number of U.S. troops based in the town were relocated to other bases in Syria, said the U.S. official, speaking on the condition of anonymity because he wasn't authorized to talk to the press.

Turkish-backed rebels have set up checkpoints on the highway near Ain Issa, cutting off the U.S. troops in bases to the west, in the Syrian cities of Manbij and Kobane. Those troops came under Turkish artillery fire Friday night in what some U.S. soldiers suspect was a deliberate attempt to drive them away from the bulk of the U.S. forces farther east, Kurdish and U.S. officials said.

With their supply lines severed, their Kurdish allies have focused on fighting Turkey and not the Islamic State. With SDF forces in disarray in many locations, the U.S. presence in northeastern Syria was rapidly becoming untenable, according to a U.S. official who spoke on the condition of anonymity because he was not authorized to speak to the press.

So was the international aid effort to assist the tens of thousands of people displaced by the fighting. With a portion of the highway under Turkish control, future aid supplies are at risk.

The Kurdish administration said all deliveries of food and medical aid have been suspended. There were indications that some agencies have begun withdrawing their staff.

A U.N. official who spoke on the condition of anonymity said half the aid workers in the areas held by the Syrian Democratic Forces have evacuated are others are expected to follow.

UNICEF and the International Committee of the Red Cross said their operations are continuing in the northeast. ICRC said it was still operating a clinic in the al-Hol camp, the largest of the many camps and prisons housing Islamic State families alongside displaced civilians.

Ain Issa is the third town from which U.S. troops have withdrawn since Trump announced that the United States would not stand in the way of a Turkish invasion of northeastern Syria aimed at pushing U.S.-allied Kurdish-led forces away from the Turkish border. Around 50 troops withdrew Monday from the border towns of Tal Abyad and Ras al-Ayn, which were the first targets of the Turkish advance.

Turkey regards the Syrian Kurdish fighters that lead the SDF a terrorist organization because of their affiliation with the Kurdistan Workers' Party, which has been waging an insurgency against the Turkish government for decades. But Turkey's offensive has drawn almost no international support, leaving the country isolated as it presses ahead with the campaign.

President Recep Tayyip Erdogan, speaking in Istanbul on Sunday, rejected foreign criticism of the Turkish offensive, as well as calls from Britain and other countries to negotiate with the Syrian Kurds to end the conflict.

"How can you recommend sitting down at the same table with terrorists?" he asked.

He said the operation would continue until the Kurdish-led force is driven back from Turkey's borders.

"We are not fighting against the Kurds," Erdogan said. "We are not targeting Kurdish citizens."

He gave no indication that the operation would end soon. Turkish forces would press 19 miles into Syria, he said, and "until they leave the space, we will continue the operation."

"We will not let a terrorist state be established in northeast Syria."

This article was written by Liz Sly, Louisa Loveluck and Sarah Dadouch, reporters for The Washington Post.