The reclusive Islamic preacher, who lives in a tiny town in the Pocono Mountains of the US state of Pensylvania, was immediately accused by Turkish President Recep Tayyip Erdogan on Friday of being behind the coup attempt.
His movement, however, denied involvement, saying in a statement that it was committed to democracy and was opposed to any military intervention.
Gulen, 75, was once a close ally of Erdogan but the two fell out in recent years, as Erdogan became suspicious of the so-called Gulenist movement's powerful presence in Turkish society, including the media, police and judiciary.
The preacher moved to the United States in 1999, before he was charged with treason in his native country.
He has since led a secluded life in Pennsylvania, declining interviews and rarely making public appearances.
The power struggle between the two foes came to a head in late 2013 after judicial officials thought to be close to Gulen brought corruption charges that directly implicated some of Erdogan's inner circle, including his son Bilal.
Erdogan launched a series of counterattacks, purging hundreds of army officers, including top generals, shutting down schools operated by Gulen's movement, Hizmet, and firing hundreds of police officers.
He has also gone after newspapers believed to be sympathetic to his rival, firing their editors or shutting them down.
Turkish authorities have accused the preacher of seeking to establish "a state within a state" in Turkey, but his movement insists he is committed to democratic reform and interfaith dialogue.
"For more than 40 years, Fethullah Gulen and Hizmet participants have advocated for, and demonstrated their commitment to, peace and democracy," the Alliance for Shared Values said in a statement on Friday.
Supporters of President of Turkey Recep Tayyip Erdogan shout slogans at the Taksim Square in Istanbul, Turkey, 16 July 2016. (AAP) Source: AAP
"We have consistently denounced military interventions in domestic politics. These are core values of Hizmet participants. We condemn any military intervention in domestic politics of Turkey."
The group said it did not wish to speculate on the unfolding crisis in Turkey and denounced as "highly irresponsible" comments by Erdogan's supporters concerning the Muslim cleric's possible involvement in the coup attempt.
According to the Anatolia news agency, around 1,800 people, including 750 police officers and 80 soldiers, have been detained as part of a crackdown against Gulen followers in the last two years.
Some 280 of them are still in jail pending trial, the agency said.
Gulen's movement advocates a mix of Sufi mysticism and harmony among people based on the teachings of Islam.
