Mr. Gulen, a mystic preacher of the Sufi branch of Islam who lives in a secluded compound in the Poconos, in Pennsylvania, has become a central point of tension between the United States and Turkey.
One Turkish official said he believed the United States played a role in the coup, an accusation Secretary of State John Kerry dismissed on Sunday as “irresponsible.” Still, in a front-page column on Tuesday, the editor in chief of a pro-government newspaper wrote, “The U.S. Tried to Assassinate Erdogan!”
At the very least, the prospect of a contentious extradition process is likely to complicate relations between the allies at a time when the United States is relying on Turkey as a crucial partner in the fight against the Islamic State.
Referring to the United States, Mr. Yildirim said, “we would be disappointed if our friends told us to present proof even though members of the assassin organization are trying to destroy an elected government under the directions of that person.” He added, “At this stage there could even be a questioning of our friendship.”
Mr. Kerry has said Turkey, as part of the extradition process, must provide evidence that withstands scrutiny in an American court — something analysts say Turkey does not have.
On Tuesday, Mr. Gulen again denied any involvement. “Turkish President Recep Tayyip Erdogan today once again demonstrated he will go to any length necessary to solidify his power and persecute his critics,” Mr. Gulen said in a statement. “It is ridiculous, irresponsible and false to suggest I had anything to do with the horrific failed coup. I urge the U.S. government to reject any effort to abuse the extradition process to carry out political vendettas.”
Turkish officials may be certain about Mr. Gulen’s actions and motives, but the nature of his movement has long confounded analysts and diplomats in Turkey, partly because the organization is opaque and individuals do not openly declare allegiance to it.
Mr. Jeffrey said it would have been hard for Gulen followers, as Islamists, to infiltrate the armed forces, which have been a stronghold of secularism in Turkey.
In diplomatic cable written in 2009, and made public by WikiLeaks, Mr. Jeffrey detailed how Mr. Gulen came to exile in the United States.
He left Turkey in 1999 after being charged with plotting to overthrow the state. The charges, Mr. Jeffrey wrote, were based on a sermon Mr. Gulen had given in which he said, “our friends, who have positions in legislative and administrative bodies, should learn its details and be vigilant all the time so they can transform it and be more fruitful on behalf of Islam in order to create a nationwide restoration.”
Mr. Gulen was later acquitted, in absentia, on all charges.
Jenny White, a professor at the Stockholm University Institute for Turkish Studies who has studied the Gulen movement, said it is centered on a worldwide network of secular schools. The goal, she said, is to create a “golden generation of young people who are educated in science, but have Muslim ethics.”
The group is socially conservative, but religious texts do not play a large role for the movement. While women are active in the movement, they are not included in decision making.
Mr. Erdogan and Mr. Gulen were once Islamist allies, at war with Turkey’s old secular elite.
After Mr. Erdogan’s Islamist Justice and Development Party came to power more than a decade ago, they teamed up to tame the military, which overthrew four elected governments last century.
A series of sensational trials, which were overseen by Gulen-affiliated judges and prosecutors and were later determined to have relied, in part, on fabricated evidence, sent hundreds of officers to prison and seemed to have secured civilian control over the military.
But three years ago, the two men had a bitter falling out as Mr. Gulen opposed the leader’s increasingly autocratic tendencies. Mr. Erdogan accused Mr. Gulen of orchestrating a corruption inquiry of top officials close to Mr. Erdogan, using the same prosecutors who had targeted the military.
Ever since, they have been enemies, and this week the government accelerated its efforts to purge the state of anyone it believes is affiliated with Mr. Gulen, or directly involved in the coup.
Ibrahim Kalin, Mr. Erdogan’s spokesman, said on Tuesday that the United States should turn him over to Turkey.
“Why hold him?” he said. “Send him to Turkey to let him go through the judicial process here and if he can prove that he is not guilty, then he can go back.”
Turks have long suspected that Mr. Gulen was an American agent, and inflaming the conspiracy theories is the fact that Graham E. Fuller, a former C.I.A. official who was once stationed in Istanbul, wrote a letter to support Mr. Gulen’s application for a green card.
Mr. Fuller, in an interview with The New York Times in 2014, said he did so on his own, not on behalf of the American government. (Funny)
In the letter, he said he wrote, to the effect, “of all the movements I’ve studied, this one is probably least likely to be a security threat.”