Mr. Gulen, in poor health, rarely leaves this bucolic spot.

Speaking over a lunch of classic Turkish food, the insistently modest Mr. Gulen, the son of a small-town imam, did not appear to be to be the type of man to wield the influence he does.

A Koran student from age 5 and preacher at 14, Mr. Gulen gradually built a vast following. He has inspired the founding of an international network of schools, hospitals and businesses. There is an Islamic bank, Asya, with billions in assets; newspapers including Zaman, Turkey’s largest daily; and a television station, EBRU-TV, in Somerset, New Jersey.

All these are part of what others call the Gulen movement but its self-effacing leader refers to as the Volunteer Movement. Mr. Gulen said it had brought him no personal gain, that his only belongings were a quilt, bedsheets and a few prized books. He said he did not know “how many countries this movement is active in, nor do I know how many teachers and students there are.”

Asked at one point about the work of his followers, he replied, “I believe that calling this movement the ‘Fethullah Gulen movement’ is not right, and doing so is disrespectful to many people dedicated to carrying out its activities. My role in this movement is very limited, and there is no leadership, no center, no loyalty to a center, and no hierarchy.”

But others say that there are more than 1,000 schools in more than 110 countries, and perhaps five million members. Emre Celik, a Turkish-Australian who presides over the Rumi Forum, a Gulen-affiliated institute in Washington, recently visited one of the more farflung schools, on the island of Zanzibar, and says more in Africa are likely. The schools are supported by wealthy Muslim businessmen.

There are several such schools in the United States, even one in Burma. They impart Islamic values but, unlike madrasas, employ the official curriculum of whatever state they are in and emphasize modern science and technology. The quality of education is considered high, and competition for spots is keen.

“He’s inspired a lot of people,” said Mr. Celik, who is trained in computer science. “People like myself, second-generation Australian Turks, the Turkish diaspora, we’re moved by his ideas.”