Very few criminal prosecutions in New York have likely drawn as much public criticism from a foreign leader as that of Reza Zarrab, a Turkish-Iranian gold trader who was charged along with eight other defendants with conspiring to evade the United States sanctions on Iran.

Turkey’s president, Recep Tayyip Erdogan, has called the charges a plot against the Turkish Republic, and raised the issue in a phone call with President Trump in September. Turkey’s foreign minister claimed that the prosecution’s evidence was concocted by Gulenists, a movement led by an Islamic cleric living in exile in Pennsylvania; the movement has been banned in Turkey as a terrorist group and blamed by Mr. Erdogan for the failed coup in 2016.

On Saturday, Turkey opened an investigation of Preet Bharara, the former United States attorney in Manhattan whose office filed the original charges, and of his successor, Joon H. Kim, who is overseeing a trial in the case that starts next week.

On Tuesday, Mr. Kim and the judge, Richard M. Berman, took the unusual step of responding publicly to the Turkish officials’ criticism.