Mr. Erdogan said Saturday that he expected to meet with Mr. Trump at the United Nations later this month to discuss military operations in northeast Syria. “There are differences between what is said and what has been done,” he said in a speech in the Turkish city of Eskisehir. “We must resolve this.”

American military and diplomatic officials declined to publicly comment on the impending deployment of about 150 troops, the final approval of which still hinges on the success of the initial joint ground patrols that are to continue in the coming days, military officials said.

A senior administration official said last month that the United States “will provide forces necessary” for northeastern Syria, noting that a platoon of a few dozen soldiers now carries out similar patrols with Turkish forces in Manbij, Syria. But it was unclear whether the new deployment would increase the overall number of American troops in Syria, or be offset by reductions in the existing force there helping directly with counterterrorism missions.

The future of northeastern Syria is just one area in which Turkey and the United States have engaged in contentious discussions.

The White House informed Turkey in July that the United States would not sell it F-35 stealth fighter jets, in retaliation for Turkey’s $2.5 billion purchase of Russian S-400 surface-to-air missile systems. The sale has also heightened the possibility of long-threatened American sanctions being imposed against a fellow member of NATO.

The United States and Turkey agreed in principle last month to establish a jointly patrolled zone for refugees along the border, but they are still negotiating the details and major differences remain.

Mr. Erdogan wants the zone to be 20 miles deep and run for 300 miles along the Turkish-Syrian border east of the Euphrates. The United States has limited Turkey’s access to a few miles. Syria has already called the plan a violation of its sovereignty and Russia emphasized the need to preserve Syria’s territorial integrity.