[Follow our live briefing as the Syrian Army raced northwest to help battle Turkish-led forces.]

But as the Americans pulled back, the Kurds moved north to try to reinforce their comrades fighting the offensive. The American soldiers could only watch from their sandbag-lined walls. Orders from Washington were simple: Hands off. Let the Kurds fight for themselves.

The orders contradicted the American military’s strategy in Syria over the past four years, especially when it came to the Kurdish fighters, known as the Y.P.G., who were integral to routing the Islamic State from northeastern Syria. The Kurds had fought in Manbij, Raqqa and deep into the Euphrates River Valley, hunting the last Islamic State fighters in the group’s now-defunct physical caliphate. But the Syrian Democratic Forces, or S.D.F., as the Kurdish and their allied Arab fighters on the ground are called, are being left behind.

American Special Forces and other troops had built close ties with their Kurdish allies, living on the same dusty compounds, sharing meals and common dangers. They fought side by side, and helped evacuate Kurdish dead and wounded from the battlefield.

“When they mourn, we mourn with them,” Gen. Joseph L. Votel, a former head of the military’s Central Command, said on Thursday at the Middle East Institute.

The Kurdish forces and American military have survived previous strains, including Mr. Trump’s sudden decision in December to withdraw all American troops from northern Syria, a decision that was later walked back somewhat.

This time may be different, and irreversible. “It would seem at this particular point, we’ve made it very, very hard for them to have a partnership relationship with us because of this recent policy decision,” General Votel said.