Bekir Bozdag told reporters at parliament that Turkey made the request after a demand for Gulen’s extradition had been made on July 19.
"We wrote and sent it, saying 'There are serious claims and expressions that Gulen has a hand in the coup attempt. That is why he needs to be immediately arrested. We have intelligence that he could flee to a third country'," said Bozdag.
Bozdag said Gulen cannot leave the U.S. without the permission or approval of the country. He added that if the U.S. gave up Gulen to another country, relations between Turkey and the U.S. would be "negatively" affected.
Bozdag said he hoped the U.S will meet the requirements of being a democratic state governed by the rule of law and extradite Gulen to Turkey.
"I think that the U.S. cannot keep such a guilty person there anymore under any circumstances," he added.
Turkey's government has repeatedly said the deadly July 15 coup attempt was organized by Gulen’s followers and his Fetullah Terrorist Organization (FETO).
Gulen is also accused of running a long-running campaign to overthrow the state through the infiltration of Turkish institutions, particularly the military, police, and judiciary, forming what is commonly known as the parallel state.