Reza Zarrab, a Turkish-Iranian national, and Mehmet Hakan Atilla, the deputy chief executive of Turkish lender Halkbank, are being held in the United States on charges of violating sanctions against Iran.
They are to go on trial on November 27, a case some commentators see as potentially damaging for Ankara.
The case was brought by the US Attorney for the Southern District of New York Preet Bharara -- who was fired this year by President Donald Trump -- and then continued under his successor Joon Kim.
Istanbul prosecutors have opened an investigation against both Bharara and Kim on the grounds that their actions "are clearly against international and domestic law".
It said that the evidence being used in the case against the "Turkish citizens" is "stolen, of fraudulent nature and unidentifiable in origin."
The move by the prosecutors comes a day after Foreign Minister Mevlut Cavusoglu blamed the case on Fethullah Gulen, the US-based preacher who Ankara considers the mastermind of last year's coup attempt.
Cavusoglu said that Gulen had succeeded in infiltrating the US justice system, describing the case as "very much FETO motivated".
Ankara accuses Gulen of running a group it calls the Fethullah Terror Organisation (FETO). Gulen's supporters ridicule the term and deny any link to the failed coup.
Cavusoglu said Bharara was "very close to FETO and he is not hiding this." Bharara shot back on Twitter: "Turkey FM is a liar. Now let's see what happens in court."
Zarrab was arrested by US authorities in March 2016 after flying with his pop star wife Ebru Gundes and their daughter to Miami for a Disney World holiday.
His detention intrigued opponents of the government in Turkey, where Zarrab had been linked to a 2013 corruption scandal that had ensnared the elite and Erdogan has denounced as a plot by Gulen to bring down his government.
The intrigue has been intensified by American reports that Zarrab is now cooperating with the US prosecutors, raising the prospect of a plea bargain that could embarrass Ankara.
Erdogan has repeatedly called for the release of Zarrab and Atilla, with the issue becoming a another bone of contention in the troubled relations between Ankara and Washington.
Trump's former national security advisor Michael Flynn is reportedly being investigated by special prosecutor Robert Mueller for alleged talks with Turkey on deporting Zarrab and Gulen in exchange for money.
Turkey and Flynn's lawyers have denied any such negotiations.