But he said Turkey's government would have to prove Fethullah Gulen's wrongdoing.
Visiting Luxembourg, Kerry said Turkey hasn't yet requested that the United States send home Gulen, who left Turkey in 1999.
Gulen has harshly condemned the attempted coup attempt by military officers that resulted in a night of explosions, air battles and gunfire that left dozens dead.
But Turkish President Recep Tayyip Erdogan's government is blaming the chaos on the cleric, who lives in exile in Pennsylvania and promotes a philosophy that blends a mystical form of Islam with staunch advocacy of democracy, education, science and interfaith dialogue.
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"We haven't received any request with respect to Mr Gulen," Kerry told reporters. "We fully anticipate that there will be questions raised about Mr Gulen.
And obviously we would 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."
"I'm confident there will be some discussion about that," Kerry added.
President Barack Obama today was briefed on the latest developments by his national security and foreign policy advisers. The White House said afterward that Obama reiterated the US' "unwavering support" for Erdogan's government, which he had done yesterday.
Gulen is understood to maintain significant support among some members of the military and mid-level bureaucrats. His movement called Hizmet includes think tanks, schools and various media enterprises. Gulen and Erdogan only became estranged in recent years.
In a statement, Gulen said he condemned, "in the strongest terms, the attempted military coup in Turkey.