But the movement’s stealthy expansion of power — as well as its tactics and lack of transparency — is now drawing accusations that Mr. Gulen’s supporters are using their influence in Turkey’s courts and police and intelligence services to engage in witch hunts against opponents with the aim of creating a more conservative Islamic Turkey. Critics say the agenda is threatening the government’s democratic credentials just as Turkey steps forward as a regional power.

“We are troubled by the secretive nature of the Gulen movement, all the smoke and mirrors,” said a senior American official, who requested anonymity to avoid breaching diplomatic protocol. “It is clear they want influence and power. We are concerned there is a hidden agenda to challenge secular Turkey and guide the country in a more Islamic direction.”

The movement has strong affiliations or sympathy in powerful parts of Turkey’s news media, including the country’s largest daily newspaper, Zaman, and, Turkish analysts say, among at least several dozen members of its 550-seat Parliament, with support extending to the highest levels of government.

With its extensive influence in the media and a small army of grass-roots supporters, the Gulen movement has provided indispensable support to the conservative, Islam-inspired government of Prime Minister Recep Tayyip Erdogan. Some officials and analysts suspect that some elements within the Gulen movement have served as a stalking-horse for the government, which has benefited, too, as the Gulen-affiliated media have attacked common opponents and backed trials that Mr. Erdogan has publicly supported.

But the relationship between Mr. Erdogan and Mr. Gulen has sometimes been tense, with the prime minster, a mercurial and populist leader, sensitive to any challenges to his authority. Analysts say that in recent months Mr. Erdogan and other members of his Justice and Development Party have grown increasingly wary, as high-profile arrests of critics of the Gulen movement have embarrassed the government. There is growing talk of a power struggle.