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Secretary of State John Kerry said that he expected the Turkish authorities to pursue inquiries against Fethullah Gulen, the cleric and opposition leader living in self-imposed exile in Pennsylvania whom President Recep Tayyip Erdogan claimed was behind Friday’s coup attempt.

“We fully anticipate that there will be questions raised about Mr. Gulen,” Mr. Kerry said at a brief news conference here in Luxembourg. “And obviously, we invite the government of Turkey, as we always do, to present us with any legitimate evidence that withstands scrutiny, and the United States will accept that and look at it and make judgments about it appropriately.”

Mr. Gulen has since 1999 lived as a recluse at the Golden Generation Worship and Retreat Center, in the Poconos. In a statement on the website of his group, Alliance for Shared Values, Mr. Gulen condemned the coup and expressed support for the country’s democratic process.

“As someone who suffered under multiple military coups during the past five decades, it is especially insulting to be accused of having any link to such an attempt,” Mr. Gulen wrote. “I categorically deny such accusations.

Turkey’s politics was for decades divided between secularists and Islamists, but both Mr. Erdogan and Mr. Gulen have occupied a middle ground between these two extremes. Beginning his career as an Islamist, Mr. Erdogan founded the Justice and Development Party in 2001 in an effort to project a less openly religious image. A moderate conservative with increasingly autocratic tendencies, Mr. Erdogan has dominated Turkish politics ever since.

While more openly religious, Mr. Gulen, 75, has promoted a more liberal stream of Islam, and his ideas are popular with the country’s police and intelligence establishments, though not necessarily the military.

He has millions of followers. Mr. Erdogan and Mr. Gulen were once allies but had a bitter falling-out in 2013 over a corruption inquiry that targeted Mr. Erdogan and his inner circle. Mr. Erdogan then purged the judiciary and the police of people linked to Mr. Gulen.

Even before the coup, prosecutors in Turkey’s capital were preparing to file an extradition request to the American authorities on charges that he led a terrorist organization and was trying to infiltrate and overthrow Turkey’s government.

Last October, an Istanbul court issued an arrest warrant for Mr. Gulen after approving a 1,453-page indictment charging him with “attempting to overthrow the government of the Republic of Turkey or obstructing it from conducting its duties by force,” according to the Anadolu, the Turkish news agency.

Also Saturday, Mr. Kerry said it was not surprising that neither the United States nor any of Turkey’s other NATO allies were aware of the coup before it occurred.

“If you’re planning a coup, you don’t exactly advertise it to your partners in NATO. It surprised everybody, including the people in Turkey,” Mr. Kerry said, “I must say it does not appear to be a very brilliantly planned or executed event.”

Mr. Kerry said that all of “our embassy personnel are 100 percent accounted for and are O.K.,” but that the process of accounting for all American citizens in Turkey continues.

He reiterated American support for the Erdogan government. “We stand by the government of Turkey,” he said.