But Mr. Erdogan, speaking at the United Nations General Assembly last month, has instead pushed for a much longer and deeper zone. A broader invasion could reach the prisons, and it would set off an armed conflict that could prompt the Kurds to pull guards from prisons so they could instead join the fight.

The “worst-case scenario” is that the Kurds are so frustrated and angered by the United States’ action that “they decide to release wholesale some of the detainees,” said Christopher P. Costa, a former senior director for counterterrorism on Mr. Trump’s National Security Council who now heads the International Spy Museum.

Is Turkey planning to take custody of ISIS prisoners?

It was not clear. The White House said Turkey would “now be responsible for all ISIS fighters in the area captured over the past two years.” But Turkey has given no public sign that it has agreed to take over that headache.

For now at least, the Kurds have told American officials that they will continue to hold the ISIS detainees. But a senior State Department official acknowledged that the best-trained guards could be pulled away in the event of a conflict with Turkey, calling it a “big concern” that some ISIS fighters could go free.

“It’s hard to imagine Turkey has the capacity to handle securely and appropriately the detainees long held by the Syrian Kurds — and that’s if Turkey even genuinely intends to try,” said Joshua A. Geltzer, a former senior director for counterterrorism at the National Security Council in the Obama administration.

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Why did Trump complain about Europeans?

The Kurds have implored countries around the world to take back their citizens who fought for the Islamic State and were captured. But that idea is politically unpopular in many European countries. Mr. Trump is correct that nations like Belgium, Britain, France and Germany have been largely content to let the Kurds bear the burden of detaining their citizens — particularly the male fighters.

Many European law enforcement officials fear that if they repatriate their extremist citizens, they would be unable to convict them or keep them locked up for a long time. European counterterrorism laws are weaker than those in the United States, where a conviction merely for joining a designated terrorist group can yield a 15-year prison sentence.