The president himself expressed second thoughts, which were, in their own way, even more jarring.

“As I have stated strongly before,” he tweeted, “and just to reiterate, if Turkey does anything that I, in my great and unmatched wisdom, consider to be off limits, I will totally destroy and obliterate the Economy of Turkey (I’ve done before!). ”

Just what, in his unmatched wisdom, Mr. Trump meant by “off limits,” or economic destruction, or the rest of the tweet was not clear. Nor is this the first time the Trump administration has sent conflicting messages about American objectives in Syria.

Last December, Mr. Trump overruled his top advisers to order the withdrawal of all 2,000 American ground troops from Syria within 30 days. The decision was ultimately reversed, but it was the final straw for Mr. Mattis.

Mr. Erdogan has long threatened to send troops into Syria. Since losing an important election in Istanbul in March, he has been under increasing pressure to find ways to shore up his domestic political support. He’d also like to resettle at least one million Syrian refugees now living in Turkey within the safe zone on the Syrian side of the border. Those refugees have become a political liability for him.

But if Kurds in Syria have to defend themselves against the Turks, they are likely to shift their forces from the fight against ISIS, including the guarding of about 10,000 ISIS prisoners now in Kurdish detention centers.

Making it possible for refugees to return home is a worthy goal, but forced resettlement is rarely successful. Moreover, many refugees in Turkey do not come from northern Syria and are unlikely to mix easily with local populations.

Whether Turkey will go forward with a full invasion is unclear. On Mr. Trump’s orders, a couple hundred American troops have been removed from two military outposts. At the same time , the Kurds have stopped dismantling their fortifications and the joint American-Turkish patrols have been ended, officials say. Congress is threatening sanctions on Turkey.