A Turkish court on Wednesday ruled to keep in jail on terror-linked charges US pastor Andrew Brunson, who ran a protestant church in the city of Izmir and has been held since October 2016.
Meanwhile, Turkey is continuing to press for the extradition of Gulen, who lives in a secluded compound in the state of Pennsylvania from where Ankara says he masterminded the coup bid. Gulen denies the charges.
The two issues, added to disputes on Syria and the detention of two Turkish US diplomatic mission staffers, have caused major strains in the relationship between the NATO allies.
"One of the aspects of the tension in the relationship has been when people, including people in the government, have drawn very direct linkages (between Gulen and Brunson)," said the official, asking not to be named.
"Very senior people have suggested that," he added. "We do not think it is appropriate to link these cases, partly because the legal systems are very different in the two countries, and the cases are very different."
In September last year, Turkish President Recep Tayyip Erdogan suggested that Turkey could free Brunson if Washington handed over Gulen in a swap deal.
"Give him (Gulen) to us, and we will try (Brunson) and give him back," Erdogan said then.
The US official's comments came after US President Donald Trump described Turkey's failure to release Brunson as a "total disgrace" and called on Erdogan to "do something" to free him.
Turkey has also expressed exasperation at the failure of the United States to hand over Gulen to face trial, although the official said there was now an increase in communication between Ankara and US legal authorities.
The official said Turkey had presented a "large quantity" of information about Gulen but said "the issue is 'is there sufficiently clear evidence of Fethullah Gulen's personal involvement in the coup?'" to allow extradition.
The official said that the United States has long kept an eye on Gulen, who has lived in self-exile in the country since 1999.
"We have been investigating the Gulen movement for longer than the Turkish government has," said the official, in an apparent dig at past cooperation between Erdogan's ruling party and the Gulen movement.
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