An Istanbul prosecutor ordered the detention of Graham Fuller, ex-vice chairman of the CIA's National Intelligence Council, as part of an investigation into the movement led by US-based Muslim cleric Fethullah Gulen and the July 15, 2016 failed coup.
Turkey accuses Gulen of masterminding the attempted putsch and has dubbed his movement the "Fethullah Terrorist Organisation" (FETO).
Gulen rejects Turkey's claims and the group denies any links to terror.
He is also suspected of "procuring information that must remain a state secret for political or military espionage", state-run news agency Anadolu reported.
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Fuller previously said in a Huffington Post piece that he wrote a letter as a private citizen in support of Gulen's green card application in 2006 because he "did not believe that Gulen constituted a security threat to the US".
His warrant is part of the same probe which has already detained prominent businessman and civil society activist Osman Kavala over links to the coup bid as well as Metin Topuz, a US consulate employee in Istanbul, Anadolu said.
Authorities on Tuesday issued an arrest warrant for Erdemir over claims he gave "fake reports" for use as evidence by US officials investigating gold trader Reza Zarrab and Mehmet Hakan Atilla, the deputy chief executive of Turkish lender Halkbank.
Zarrab was arrested last year but has now agreed to be the prosecution's star witness in a potentially explosive New York trial over whether Turkish individuals including Atilla violated US sanctions against Iran.
The case has provoked Erdogan's ire and added tension to Ankara-Washington relations, already strained by the US failure to extradite Gulen.
Turkish officials, including Erdogan, have called the case a "plot" against Turkey pushed forward by Gulenists in the US.