Mr. Erdogan predicted in a television interview this year that a private dialogue between Berat Albayrak, his son-in-law and finance minister, and Mr. Kushner would soon put “back on track” the vexed relations between Washington and Ankara. “The bridge works well in this manner,” Mr. Erdogan said.

“Backdoor diplomacy,” Mr. Albayrak called his work with Mr. Kushner.

Mr. Trump’s policy toward Turkey has confounded his fellow Republicans in Congress on a number of fronts. Mr. Trump twice surprised his own advisers by agreeing during phone calls with Mr. Erdogan to pull United States troops from northern Syria — and the second time, in early October, he followed through, clearing the way for Turkish forces to attack an American-backed militia there…

The term “deep state,” in fact, first emerged in Turkey decades ago, long before it came into vogue among Trump supporters, and Mr. Erdogan’s advisers say he has cultivated Mr. Trump by emphasizing their shared struggles against such entrenched forces within their governments.