Until 2013, Gulen was an ally of Erdogan, when their relationship broke down over a corruption scandal. Gulen has since been on Turkey`s most-wanted terrorist list.
Gulen a cleric, now lives abroad, and leads a popular movement called Hizmet.
Hizmet is a global initiative, described by the New York Times as "a moderate, pro-Western brand of Sunni Islam that appeals to many well-educated and professional Turks".
It has founded schools, tutoring centres, hospitals and relief agencies.
Supporters describe Gulen as a moderate Muslim cleric who advocates interfaith dialogue.
President Erdogan has levelled the finger of blame for Friday`s coup squarely at Gulen.
In a bid to get him extradited to Turkey President Erdogan said: "I call on the United States and President Barack Obama. Dear Mr. President, I told you this before.
Either arrest Fethullah Gulen or return him to Turkey. You didn`t listen. I call on you again, after there was a coup attempt.
Extradite this man in Pennsylvania to Turkey! If we are strategic partners or model partners, do what is necessary,"
Gulen denies any connection to the coup attempt and has suggested the whole thing may have been staged.
The US has said it is willing to help Turkey investigate who is behind the coup, but will only act against Gullen if there was evidence against him.
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