Mr. Gulen, 73, has millions of followers around the world, and his supporters in Turkey hold positions of power in the police force and the judiciary. The arrests on Wednesday follow a string of orchestrated raids on institutions linked to Mr. Gulen’s supporters, and they represent the latest attempt in Mr. Erdogan’s campaign to root out Mr. Gulen’s influence before general elections scheduled for June.

Image Fethullah Gulen, an exiled cleric and rival to President Recep Tayyip Erdogan. Credit... Selahattin Sevi/Reuters

In 2013, Mr. Erdogan accused Mr. Gulen’s supporters of pursuing a corruption scandal against him that implicated members of his inner circle. Recordings from illegal wiretaps of Mr. Erdogan when he was the prime minister were posted on social media sites in what Mr. Erdogan called an attempt staged by Mr. Gulen to bring down his government.

The Turkish government has since purged thousands of Gulen supporters from the ranks of the police force and the judiciary.

Since December, Turkey has issued two arrest warrants for Mr. Gulen, who has lived in the United States since 1999. The most recent request for a warrant was made on Tuesday by the Istanbul Public Prosecutor’s Office, which accused Mr. Gulen of being a member of a terrorist organization and of forming a “parallel state” to overthrow the government.

The first warrant, issued in December, accused Mr. Gulen of committing a crime, without providing further details. Mr. Gulen has denied playing a role in plots against the government. The warrants are thought to be an effort to form the basis of a formal request to the United States for Mr. Gulen’s extradition.