Those named in the orders included three active-duty captains serving at the General Command of the Gendarmerie.
The list also included seven majors and 10 captains who had previously been subject to administrative or judicial proceedings.
The supplied report did not identify the remaining three people covered by the detention orders.
Turkish authorities have frequently cited alleged periodic or consecutive calls from payphones or other public phones as evidence in investigations targeting people accused of Gülen movement affiliation.
Ankara blames the coup attempt on the Gülen movement, a transnational civic initiative inspired by Islamic scholar Fethullah Gülen, and designates the movement as a terrorist organization. The movement denies involvement in the coup or any terrorist activity.
