However, most analysts say his adherents are entrenched within the Turkish state, where they are in a position to do a great deal of damage if they so choose. The crisis actually stems, many say, from a fallout between Mr. Gulen and Mr. Erdogan, who were once allies in the current Islamist governing coalition.

Now that they are warring, many Turks say they are caught in the middle of a power struggle.

“There is no way of knowing whether the tapes are real or fake,” said Ince Unaldi, who works in a women’s clothing boutique in the affluent Etiler district of Istanbul, after listening to the latest leak. “We are being dragged into a war of two very dark forces.”

In a statement, the Rumi Forum, a Washington-based center for interfaith cooperation of which Mr. Gulen is honorary chairman, said on Tuesday night that “Mr. Gulen has no connection whatsoever with any phone tapping, including that of the prime minister and his son that was revealed yesterday.”

For many Turks the scandal, and the manner in which it has unfolded, have become something of a preoccupation. On Tuesday, after spending Monday night riveted by the latest leak, Kaya Genc, a novelist and essayist who lives in Istanbul, was up against a deadline for an essay he is writing for the Paris Review. But he was glued to his television set, watching Mr. Erdogan speak to lawmakers from his Justice and Development Party in Ankara, the Turkish capital.

For Mr. Genc, the situation, and his inability to focus on his work amid the drumbeat of scandal, brought to mind a quote from the famous Turkish novelist Ahmet Hamdi Tanpinar, whose 1960s-era comic novel “The Time Regulation Institute” was recently published in English: “Turkey does not allow its children to care for anything besides its own problems.”

He added: “It’s like a TV series they watch after hours. In the morning, they come to their senses and say, ‘What was that all about?’ But in the evening it is entertainment. ‘The Magnificent Century’ is the only thing that rivals these things.”

On Monday night Ozgur Unluhisarcikli, the director of the Ankara office of the German Marshall Fund of the United States, a research organization, was reading a book and trying to unplug from social media for one evening. But the electricity went out, and with nothing else to do he got on Twitter and saw the uproar over the latest leak.