President Recep Tayyip Erdogan of Turkey accused President Trump on Friday of having broken with “diplomatic and political courtesy” by sending him a letter threatening to destroy the Turkish economy if he did not behave in “the right and humane way” in Syria.

“We will not forget this lack of respect,” Mr. Erdogan told reporters in Istanbul. “But our reciprocal love and respect,” he said, would prevent the two leaders from keeping the letter “continuously on the agenda.”

At the same time, Mr. Erdogan said, “we also want it to be known that, when the time comes, the necessary thing will be done.’’

It was the latest back and forth between the two leaders who have sought to portray themselves as strong-willed and unforgiving, and created an intensely personal backdrop for a policy decision with deadly serious consequences.