Fethullah Gulen has lived in self-imposed exile in Pennsylvania since 1997, when secularist authorities raised accusations of Islamist activity against him. Erdogan accuses him of building a "parallel state" of followers in institutions such as the police and judiciary and using them to try to pull the levers of state power.
Gulen, a former ally, denies engineering a police graft investigation which has seen three cabinet ministers quit, but has denounced Erdogan over moves to shut down the inquiry by purging police and judiciary of his followers.
Asked by a reporter at parliament after a meeting of his ruling AK Party if a process would begin for Gulen's extradition, Erdogan said: "Yes, it will begin."
In an interview with PBS talk show host Charlie Rose broadcast late on Monday, Erdogan said Gulen could also pose a threat to US security by his activities.