Erdogan accuses Gulen and his supporters of using influence within the judiciary, police and state bureaucracy to plot against the government.
In an intensification of the campaign against his movement, Turkish banking authorities this week seized control of Bank Asya, an Islamic bank founded by followers of Gulen.
"Of course he should be extradited. There is already an agreement between Turkey and the United States. There are international treaties," Foreign Minister Mevlut Cavusoglu said, quoted by the official Anatolia news agency.
Turkey and the United States signed an extradition treaty in 1979, but legal experts say that a crime requiring extradition must be recognised in both countries.
In December, an Istanbul court issued an arrest warrant for Gulen, accusing him of setting up and directing an "armed terrorist organisation."
But the United States has so far paid little attention to repeated requests from Turkey for Gulen's extradition from his secluded compound in the state of Pennsylvania.
Gulen leads a broad powerful movement known as "Hizmet" (Service), believed to be supported by millions of Turks and which brings together interests ranging from finance to schools to media.
Gulen, who left for the US in 1999 to escape charges of anti-secular activities by the government at the time, has denied being behind the graft allegations against Erdogan.
But Erdogan has vowed to press his battle with Gulen, purging the police force and judiciary to rid them of pro-Gulenist elements.
Erdogan's opponents had denounced the seizure of Bank Asya as a blatant political manoeuvre against Gulen. But the government vehemently denied this was the case.