Ankara accuses Gulen of masterminding the coup, during which a rogue military faction tried to oust President Erdogan.
Turkish Justice Minister Bekir Bozdag said the suspects had been placed under arrest since the attempted putsch that fell apart within hours, quoted by NTV broadcaster.
"Another 3,907 suspects were still being sought while nearly 26,000 people had been released into "judicial control", he said.
Some 82,000 individuals had been investigated in total since the coup bid, he told the audience on Saturday at a ruling Justice and Development Party conference in Afyonkarahisar, western Turkey.
Tens of thousands of people have been suspended, sacked or detained in the military, judiciary, police, education sector and media in connection with the July 15 attempted putsch blamed on Gulen and his Hizmet (Service) movement.
The unprecedented purge has come under heavy criticism from Turkey's Western allies, including the European Union. Brussels has urged Ankara to act within the rule of law, which Turkey insists it is.
Ankara accuses Gulen of masterminding the coup, during which a rogue military faction tried to oust President Recep Tayyip Erdogan.
Gulen -- who has lived in self-imposed exile since 1999 in Pennsylvania -- strongly denies the charges.