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The Turks put the focus on academics, which pleased Mr. Bari, who said his dream was for Saadudeen, his brother, to lift the family out of poverty and expand its horizons beyond religion. Mr. Bari’s title, hafiz, means he has memorized the entire Koran, though he has no formal education. Two other brothers have earned the same distinction. Their father was an imam.

His is a lonely mission in a neighborhood where nearly all the residents are illiterate and most disapprove of his choices, Mr. Bari said. He is constantly on guard against extremism. He once punished Saadudeen for flying kites with the wrong kind of boys. At the Turkish school, the teenager is supervised around the clock in a dormitory.

“They are totally against extremism,” Mr. Bari said of the Turks. “They are true Muslims. They will make my brother into a true Muslim. He’ll deal with people with justice and wisdom. Not with impatience.”

Illiteracy is one of the roots of problems dogging the Muslim world, said Matiullah Aail, a religious scholar in Quetta who graduated from Medina University in Saudi Arabia.

In Baluchistan, Quetta’s sparsely populated province, the literacy rate is less than 10 percent, said Tariq Baluch, a government official in the Pasheen district. He estimated that about half of the district’s children attended madrasas.

Mr. Aail said: “Doctors and lawyers have to show their degrees. But when it comes to mullahs, no one asks them for their qualifications. They don’t have knowledge, but they are influential.”

That leads to a skewed interpretation of Islam, even by those schooled in it, according to Mr. Gulen and his followers.

“They’ve memorized the entire holy book, but they don’t understand its meaning,” said Kamil Ture, a Turkish administrator.

Mr. Kacmaz chimed in: “How we interpret the Koran is totally dependent on our education.”

In an interview in 2004, published in a book of his writings, Mr. Gulen put it like this: “In the countries where Muslims live, some religious leaders and immature Muslims have no other weapon in hand than their fundamental interpretation of Islam. They use this to engage people in struggles that serve their own purposes.”

Moderate as that sounds, some Turks say Mr. Gulen uses the schools to advance his own political agenda. Murat Belge, a prominent Turkish intellectual who has experience with the movement, said that Mr. Gulen “sincerely believes that he has been chosen by God,” and described Mr. Gulen’s followers as “Muslim Jesuits” who are preparing elites to run the country.

Hakan Yavuz, a Turkish professor at the University of Utah who has had extensive experience with the Gulen movement, offered a darker assessment.

“The purpose here is very much power,” Mr. Yavuz said. “The model of power is the Ottoman Empire and the idea that Turks should shape the Muslim world.”

But while radical Islamists seek to re-establish a seventh-century Islamic caliphate, without nations or borders, and more moderate Islamists, like Egypt’s Muslim Brotherhood, use secular democracy to achieve the goal of an Islamic state, Mr. Gulen is a nationalist who says he wants no more than a secular democracy where citizens are free to worship, a claim secular Turks find highly suspect.

Still, his schools are richly supported by Turkish businessmen. M. Ihsan Kalkavan, a shipping magnate who has built hotels in Nigeria, helped finance Gulen schools there, which he said had attracted the children of the Nigerian elite.

“When we take our education experiment to other countries, we introduce ourselves. We say, ‘See, we’re not terrorists.’ When people get to know us, things change,” Mr. Kalkavan said in his office in Istanbul.

He estimated the number of Mr. Gulen’s followers in Turkey at three million to five million. The network itself does not provide estimates, and Mr. Gulen declined to be interviewed.

The schools, which also operate in Christian countries like Russia, are not for Muslims alone, and one of their stated aims is to promote interfaith understanding. Mr. Gulen met the previous pope, as well as Jewish and Orthodox Christian leaders, and teachers in the schools say they stress multiculturalism and universal values.

“We are all humans,” said Mr. Kacmaz, the principal. “In Islam, every human being is very important.”

Pakistani society is changing fast, and more Pakistanis are realizing the importance of education, in part because they have more to lose, parents said. Abrar Awan, whose son is attending the Turkish school in Quetta, said he had grown tired of the attitude of the Islamic political parties he belonged to as a student. Now a government employee with a steady job, he sees real life as more complicated than black-and-white ideology.

“America or the West was always behind every fault, every problem,” he said, at a gathering of fathers in April. “Now, in my practical life, I know the faults are within us.”

Sebnem Arsu contributed reporting from Karachi and Quetta in Pakistan and from Istanbul.