It appeared the Islamic State had suffered a stunning defeat, its first major reversal since it was driven out of the Iraqi city of Tikrit in April, and one that could prove far more consequential. Tal Abyad commands the major trade and smuggling routes on which the Islamic State has relied for its supplies from the outside world and, most significant, the flow of foreign fighters to Raqqa, the first major city it conquered.

If the Kurdish-led force consolidates its hold over Tal Abyad, “it will be a major setback for the Islamic State and a major strategic victory,” said Jennifer Cafarella of the Washington-based Institute for the Study of War.

The militants may be planning a counteroffensive, “and it will be interesting to see what they do in the coming week,” she added.

But there were also signs that at least some Islamic State fighters had simply given up.